If I'm not one of those players sprinting everywhere, how can I be effective if my play is a bit slower paced? Is there any chance of competing against high-speed play (particularly with respect to movement) without doing the same?
Run and gun is about one thing - traversing the most often-traveled areas of a map quickly (hot zones), to encounter and ideally dispatch as many targets as possible. If this is not your style (it is most people's), you best course of action is to play directly against this behavior - effectively, play anti-run and gun.
The first key element to anti-R&G that you'll have to worry about (and really this is an advantage all the time, but with R&Gers speed it's even more relevant) - you don't want them to know where you are. If an R&Ger's dot/indicator shows up on a minimap, it's probably no big deal to them - they're already dead, or running away from that spot. You, however - you're a prime target for all the R&Gers in the area, instantly. Another key point here is that camping is probably a bad idea - you might get one kill, but there's a good chance that player is going to come looking for you.
The second key element is knowing where they are (or will be), and using that to your advantage. Getting to know the maps very well is incredibly important - specifically, the spots that are less often traveled, have good cover, where you can't be easily seen by someone moving quickly, or that allow good line of sight to major walkways (without being in a major walkway themselves) are the best. You don't want to stay in these spots long, however - after you get a kill or two, head in a safe direction under cover to another good spot.
To combat the run and gun "lifestyle" of the mercenary / ninja sprinter types requires a little tactical game play methodology, planning and strategic maneuvering around maps.
This answer may seem long... but we're talking about competitive game strategy!
Overall, I wouldn't recommend camping AKA staying in one spot and trying to return to it all the time after each spawn. People will learn your pattern right away and just run up and gun you in that corner you're always in.
You need to be able to use ANY place on the map intelligently, evaluating the players in the match and the space you're in. If you can learn THEIR patterns, you CAN defeat them.
rotate between movement and rest.
Learn players patterns, and cut them off.
Move around the map.
Run to and from places.
learn to crouch, walk and scope dive, effectively, to move around the map.
Let people move into your line of fire, vs moving into theirs.
Keep your gun UP. Head shots vs getting shot in the toe - do the math.
KNOW THE MAPS. Knowing the maps inside and out is key. Go into a private match and just spend time really knowing the map. Know the explosive barrels, cars that blow up, and all the places where you can use cover to effectively clear other people out before moving to your next point of attack/defense.
MOVE Instead of dashing around and looking for kills, you let them come to you and you position yourself to be somewhere different after you clear a few kills out of a fire fight.
THEN you DASH off and instead of camping you're reloading, switching weapons and laying down claymores or the ever effective IMS... keep moving and have a plan. Evaluate your surroundings.
know the traffic flows. Knowing where people are forced to traverse in the maps is key. Leaving an IMS in a tight spot insures at least 4 kills. It also protects your equipment from being destroyed at long range.
Maneuver from one piece of cover where you are able to control the angles and cross fire and most important, be able to DASH out if someone is on to you.
HAVE A PLAN. Don't run wild, run to a spot with cover. Did someone spot you? Go around the corner and flash bang them, or just scope up and wait for them to walk through. Did they toss out a flash or grenade? move further back or around cover keeping the angle set in your line of fire for them to walk into it, and not you move into their sites.
Know thy enemy run and gun types do indeed look for traffic jams and hope to rack up kills. They circle spawn points and almost always get "first blood" as they know immediately to their left/right/front/back is a person who is starting out. They typically fly out the gate at spawn and run right back to the fire fight. Exploit this. Wait for them. Kill them in their haste.
Dont Run! A lot of people start out every spawn in a sprint. Almost always running through someone's line of sight. And they end up getting shot in the back, stalked and killed, or just blasted as soon as they spawn. Be patient and give yourself a second to let someone else give their position away. Don't dash out with them in a race to kill or be killed.
RUN and SCOPE! After you kill someone, or have a little battle, RUN don't walk to a spot with cover and quick scope up to look around. Is there a blind corner coming up? Scope up? Walking up a hill? Scope up? Bunch of red dots fire fighting where you're headed? toss grenade and SCOPE UP! Keeping your gun up in transit and being ready to shoot and pull into scope helps! You're focused and aiming, while others are often just running and shooting from the hip.
Weapon classes! Playing a small map? Carry a SMG with extended clip and rapid fire. Carry a secondary machine pistol like the scorpion. Playing a larger map but getting stormed? SWITCH classes to something light and mobile so you can move OUT of their way and around cover and clear them out.
Be the enemy If you find yourself getting run over by a player with a certain weapon, and you keep your setup the same : CHANGE IT. Play their weapon and learn why they are effective at what the do. STUDY THEM. You'll find that fast players often are light weaponed and under protected. Learn to side step and knife them.
GRENADES and flash bangs! Got a pack of players attacking you? grenade those bastards. Out of grenades? flash bang them and step around or behind and mow them down.
KNIFE! People running up on you? MELEE that ass. Nothing says "Back up homie" like a lunging knife. knife takes priority over a recently drawn weapon.
Speed PERKS! Nothing like keeping up w the joneses... add slight of hand, ninja, marathon and combine this with lighter automatic weapons. I personally have found the SMC assault rifle paired with a UMP45 or scorpion after getting overkill and using slight of hand pro or blind eye pro, ninja pro and stalker pro is effective. Adjust your perks and weapon proficiencies to also be fast. It doesn't mean you need to run and gun, but it doesn't mean you should lose time reloading, switching weapons or that you should BE slow in actual movement.
Kill streaks! Not getting a lot of consecutive kills and want to lay down that bombin run? Switch to SUPPORT and your kill streak climbs EVEN IF YOU DIE. I use the UAV, Booby trapped care package, and stealth bomber. if it's not working... switch it up.
Learn patterns! Most players have only 1 or 2 patters of travel. Smart players adapt to who is trying to hide where on a map. They change routes and aren't predictable.
Choose your battle! Sometimes it isn't worth digging someone out. many players lie in wait for you to come back to a spot after they've killed you. They'll go from being a sniper in a window to laying prone facing the doorway waiting for you to come in. They know you want to come back and get revenge. Maybe cooking a grenade and tossing it into a window is better than running up stairs and confronting them head on.
Multiple game types If you are only playing a few or one game type, try playing other game types with different objectives. Lately I've been playing sabotage but I've been playing it to work on strategically eliminating players to get kills, meet daily challenges and to level up.
Think about something else Go look in the barracks under challenges. If you're getting frustrated trying to get kills, think about a different type of goal. Work towards something easy and build your skill. IF you're getting really worked up, cut off that game and go outside, hang with the loved ones or build that model in a bottle. You'll come back refreshed and ready for the challenges ahead.
You can rack up frags even if you are slow. Run & gun type players rely on the element of surprise. If you expect them coming round corners, and they don't know you are there, you can beat them at ther own game.
This is mostly known as camping a certain spot, and the next time they come for you, they will throw in a nade first, so be prepared for that, too.
Use heavy guns.
Use a shotgun or a rocket launcher when you are at places you can be attacked at. If you can't aim well, you can at least press the trigger and hope for a kill.
Let them come to you. Do not go to them. Walk around only to travel from one camp spot to another, and check all sides while in the open. Cover your back while you are waiting. And leave only one entry point if possible. Claymores might be helpful.
Keep your distance
Play as a sniper, and stay out of the trouble. That is, find yourself a corner and try to shoot passer-bys. Most people shoot only at the moving targets. Make use of perks like Assassin.
And finally, be ignorant.
You will be called a lame camper and you will possibly be kicked out of certain servers, but if this is really your playstyle, you better take it okay.
There are a few good, hard counters to the run-and-gun playstyle. A few I would recommend for you are:
1) Don't sprint
It's in their name, run and gunners are almost always sprinting, and a simple fact of COD is that 9/10 times if two players of equal skill (and connection) come face-to-face, and one was sprinting, the non-sprinter will win the engagement. Concentrate on not sprinting in heavy traffic areas or around corners.
2) Learn the maps inside out.
It sounds obvious, but knowing where you're getting killed from by run-and-gunners is key. In previous COD games the heavy traffic, popular lines of sights etc were easy to learn and obvious. In MW3, not so much due to almost every location having multiple flanks etc. I'd recommend turning your theatre mode on and watching at least a couple of games per map. Take note of where you're dying - was it because you were flanked? Were you not expecting anyone to fly around that corner?
3) Turn your tv up, or get a headset.
Listen for footsteps. In MW3 run and gunners have a very difficult choice for their third perk. In previous CODS it was ninja all the way, now you'll find a very large amount of run and gunners will sacrifice that for stalker or (in my case) steady aim, since hip firing is so woeful without it, and run-and-gunners love to hipfire
4) Play and position yourself to your class strengths:
This DOES NOT mean camp. In my opinion, camping is not only not a very fun way to play, but its a sure-fire way to get revenged, and throw in all the current hoopla with lag compensation, more often than not staying still will be to your detriment. What I mean by this is play your class' strengths. If you're getting killed by run-and-gunners because you're using an lmg in a small, close quarters space, that's your fault, and you're gifting them the kill. Almost all the maps have alternate routes lending to different styles of play. If you're using assault rifles, take the longer line-of-site routes than if you're using an smg/shotgun for example.
5) Use your teammates:
Assuming that you're playing team based games, always know where your team is, and where you're spawning. If you're moving around the map with a teammate (which I very highly recommend), be aware of which ways they're looking and checking, and make sure you check the opposite. If you're with a group, chances are the run-and-gunner will kill someone else, in which case you're tipped off by the radar or the teammated-killed-skull-thing. Don't stack up though, that's a recipe for a double/triple death.
6) Use anti run-and-gun killstreaks and equipment
I would suggest a claymore or bouncing betty as your equipment. As a secondary, I'd recommend a machine pistol, so if you get tipped off that a runner is approaching in a close quarters area, you can switch up if your main weapon isn't suitable. For killstreaks, you really can't go past a UAV. Obviously, there are always a few with assassin, but with the other Red perks so good, there's always a good chance quite a few won't be hidden. IMS and sentry guns are very handy for covering your back, and an Overwatch (if you're comfortable reaching 9) will be invaluable for catching runners coming up on you. Otherwise for support UAV, Vests (can't believe how underused they are) and any other of your choice. As for perks, honestly it won't matter too much in my opinion, but if I had to give a recommendation it would be Recon, quickdraw + probably steady aim. Recon allows you to toss a flash into/out of a room if you suspect you're being rushed. Quickdraw and steady aim will help you get the jump on them if they fly around a corner.
7) Have fun
While all these recommendations are nice, remember to ultimately play the game the way you want to. If you're getting frustrated, try something different. Muck around with the riot shield or desert eagle or rpg. I have a specific class called 'fun' that is designed for mucking around and getting awful k/d's. The truth of it is, while it's easy to come up with theory for beating certain playstyles, you only get better with practice and experience, so make sure you enjoy the time you're playing.
There is an art to camping. Forget all the crap about it not being fun, shooting fish in a barrel is truly a man's sport.
That being said, how to counter the R&G crowd?
Play objective games (like Domination)
Yep, you know where A, B, and C are and you shoot the fish in the barrel. Don't play their game. Stay back and whack the moles going for the objective. I personally use an LMG with a scope and just spray'n'pray. Let them walk right into it.
Watch, Listen, and Pray
Watch your mini-map. When you see a bunch of red dots swirling, set-up shop outside their line of site and start shooting.
Listen for footsteps (you'll hear them coming...)
Pray -- and accept the fact that you'll get whacked a few times in your Camp Snoopy position. Who cares, even the best players get killed.
Piss them off and make them pay
Yep, nothing better than to camp and kill. 8/10 times, they're coming back to get you. USE THAT TO YOUR ADVANTAGE. It's human nature. You just pissed them off, they aren't thinking rationally, it's revenge time. Excellent fool!
After a camp kill, immediately get up and move to a position 45 to 180 degrees opposite. When they come back you simply pick them off again. Now they are really pissed. Excellent! Do it again. I bagged one guy 6 times by moving around the room randomly. Suckers...
Use Last Stand (or whatever it's called)
Nothing feels better than to kill that R&G'er after his death shot doesn't kill you. Yeah, he's coming back but have a ready supply of flash bangs or nades going to the entry location.
Acceptance Some maps are really hard to camp. Hard, but not impossible.
Shoot Early Always shoot early. Never try to time your shot. Lag sucks and to counter it, shoot early and slightly ahead of movement.
Never, Never, Never Play Their Game Look, R&G'ers are experts. Don't ever try to play their game. Accept your limitations and know your strengths. If you let them goad you into their style, they'll kill you every time. Make them pay, not you.
Wow, a lot of well-thought answers of great length. They are all nice answers, but really, this is the correct one: have a good connection to the host.
This game is incredibly weighted by connection to the host. If you have a good one, you'll succeed; if you don't, you won't. It's that simple. I can play incredibly and go 15-10 because I constantly get screwed out of kills (shooting first and insta-dying after you get 3 hit-marker, for example).
Do yourself a favor: don't camp. It's a dirty little habit and you won't feel great about the kills. Sitting in a window, target-shooting isn't really fun and you're not earning your kills. You're just getting them because they happen to stumble into your sights. Move around the map, using the cover and nuances of the environment and you'll enjoy it a lot more. Laying prone in the grass is booooooring. It's better to go big-game hunting than to wait for a mouse trap to snap.