In all Pokemon versions, there's a trade off: You can easily level a few Pokemon off of trainers, or slowly grind to level your entire team.
With the goals of beating the game and catching as many possible, what's the best strategy for efficiency in terms of the number of Pokemon you train throughout the game?
What about HM slaves?
For example, should one only focus on three pokemon from the beginning to end game?
I have never thought of the Elite 4 as "End Game," just as I never though of hitting level 60 (and later 70, 80, 85) as "End Game" in WoW. Rather it was just another stepping stone. Because of this attitude, I optimized very differently.
First, I found that 3 Pokemon was about the sweet spot for training at a time. Usually this entailed 1 or 2 (xp share, or swapping) I was focusing on, and a third for backup (someone beefy enough to roll whatever area I was in).
Next, I specifically targeted Pokemon whose EVs I could easily raise. There are a couple areas where you can guarantee which EV you'll get, but usually I lead with a Pokemon whose EVs I didn't care about, and then swapped according to what I ran into (in the case of trainers I could set this up more intelligently). As a result, I was usually targeting only 1 or 2 for actual EV leveling. This process would recur every time I got a Pokemon whom I wanted to level (I usually decide these at game start).
Once a Pokemon had been EV leveled, I could then use it as a clean up for other Pokemon's EV leveling. From a pure XP perspective, having a "clean up" Pokemon (sometimes initiator) means that that Pokemon will be receiving more than its fair share of experience. The end result is that usually the Pokemon that I EV train first end up being my strongest (not just because of EVs).
Finally, as I originally stated my end goal is not the Elite Four; rather I'm eventually targeting competitive play. However, EV training other Pokemon doesn't max out my first couple, so ultimately I end up doing runs on the Elite Four to power level them fast. Usually, by the time I hit my first run I have 4-5 beefy Pokemon fully EV trained, so it's not a major challenge. However, sometimes I haven't spent enough time and that usually means I need to take the time to EV train up a couple more Pokemon so they hit that sweet spot where they start firing on all cylinders.
I realize this may not be exactly your use case, but I think it is something to keep in mind.
With the goals of beating the game
If your only goal is to beat the Elite Four the first time, you can do it reasonably quickly with three or four Pokemon planned carefully to cover each other's weaknesses (plus lots of items if they're low level). In the later games, when you challenge the Elite Four a second time, their Pokemon are stronger and higher level, and if you want to beat them the second time then I recommend four or five. I've never actually tried four, but five is enough; with planning you should never need six. (That frees a slot for an HM slave at all times.)
Ultimately, I think planning is probably more important than the exact number you use. For example, in any game where you can find Woopers early, Quagsire is a great addition to a team: Water and Ground are both great offensive types, and defensively Quagsire's only weakness is 4x to Grass. A Quagsire and a Typhlosion already cover each other's weaknesses almost perfectly.
EV training strikes me as overkill for going through the game. It's not very fun, takes a long time (unless you have the various magic things that make it take less time), and I've never needed to do it to beat the Elite Four. The Pokemon that are best for going through the game are, for various reasons, not generally the best for competitive play, so even if your ultimate target is competitive play it seems like a better idea to wait until after the Elite Four to work on it.
I know this question is damn old, but since this has changed considerably in Gen VI, I wanted to add another answer pointing out the new go-to strategy.
As of Generation 6 (X/Y), Exp. Points are no longer split between Pokemon. Instead, as has always been the case with EVs, every Pokemon involved in the battle will get the full amount of Exp. Points.
Additionally, the Exp.Share is now a key item that grants half that amount of Exp. Points to any Pokemon in the party which was not involved in the battle. It can be turned on and off.
To illustrate: Suppose I have 2 Pokemon with me, Bulbasaur and Pidgey. I run into a wild Pokemon and defeat it with Bulbasaur, gaining 40 Exp. Points. I then run into another Pokemon of the same species at the same level. I switch Bulbasaur out for Pidgey and defeat the wild Pokemon. Now Bulbasaur and Pidgey will each receive the full 40 Exp. Points (in previous generations, they would receive 20 each). This is the same no matter how many Pokemon you send into the battle. If I now decide to turn on my Exp. Share (which you receive automatically after beating the first gym) and again run into one of these wild Pokemon and defeat it with Bulbasaur, then Bulbasaur will receive 40 Exp. Points and Pidgey 20 (which is not explicitly displayed). If I had 6 Pokemon in my party, Bulbasaur would still receive 40 Exp. Points and each of the other Pokemon in my party would receive 20 Exp. Points.
What this means is that as of Generation 6, you make the best out of the Exp. Points you get on your run by carrying as many Pokemon as possible and either switching all of them in or turning Exp. Share on. If you care about efficiency, try to catch 5 additional Pokemon before the first gym and ignore them all along, leveling only your Starter. Then once you get Exp. Share, turn it on and watch the rest of your team catch up to the Starter. You also get Lucky Egg rather early, so you can give that to the other Pokemon in your party to make them catch up faster. Once they're sufficiently strong, you can switch them around and shift the focus of the full amount of Exp. Points so that your team levels evenly. That way, even beating the Elite Four without any kind of preparation is very possible because you will be ridiculously overleveled.
As an added bonus, some of the Pokemon you can get early in X and Y are very powerful, even the new early game bug (Scatterbug/Spewpa/Vivillon) is a good addition to your team (unlike in previous generations, where the bug you got early was rather useless after level 30).
In the first four games or so, I trained about 4 pokemon at a time. Sometimes I switched out my extras for necessary HM's, or ones that could survive in a gym fight. Honestly, all you truly need is 1-2 pokemon to beat gym trainers, as long as you are using the opposing element of that gym leader. Of course, to beat the elite four (in the first few games), you need all 6 pokemon usually.
Your best goal, if your main focus is efficiency, is to never switch Pokemon. Catch only what you're going to use, catch it early, and never switch to something new. This way you don't waste any experience on Pokemon that aren't in your final party, and they can get a head start gaining experience as soon as possible.
The problem with this approach is that the Pokemon you can get early tend not to have very much variety and you'll probably have trouble against the Elite 4 with only low-powered early Pokemon. From my numerous play-throughs, the sweet spot seems to be about 4 Pokemon. You don't have to wander through the grass for hours at a time making sure one of them isn't worthless, and you'll still be plenty powerful and versatile for most of the battles you come across.
The Elite 4 is generally never easy the first time without some grinding or ridiculously thorough planning beforehand, though.
