Many of the older games in the Metal Gear series were released before the modern trend of pre-order bonuses and collector's editions and such. All of the following games
- Metal Gear
- Metal Gear 2: Solid Snake
- Snake's Revenge
- Metal Gear Solid
- Metal Gear Solid: Integral
- Metal Gear: Ghost Babel
- Metal Gear Solid 2: Sons of Liberty
- Metal Gear Solid 2: Substance
- Metal Gear Solid: The Twin Snakes
had no pre-order or collector's edition content of any notable form, in any version or format they were released in (that I'm aware of or have been able to track down).
Metal Gear Solid 3: Snake Eater was the first game to have such content. The original Japanese release (which shipped after the North American release) allowed you to download a unique camo skin, and there was a limited-edition package for sale in Japan that included some physical extras. Pre-ordering in Japan got you a disc with some extra camo skins on it as well, in addition to access, via cell phone, to a site offering downloads of images, music, and more camo skins. The European release of the game included some extra gameplay modes (a boss rush mode, cutscene replay mode, the "Snake vs. Monkey" mini-games, and some facepaint camo).
The majority -- or possibly all -- of these camo skins and features were made available in the Metal Gear Solid 3: Subsistence re-release. Subsistence includes the first major piece of content you won't be able to access any longer: it shipped with a multiplayer mode called Metal Gear Online, which was discontinued in 2006 is is now unavailable. Limited-edition copies of Subsistence were also sold with some extras, mostly videos and documentaries and the like.
Metal Gear Solid 4: Guns of the Patriots had bonus packages that mainly featured physical items, including a bundle with a special PS3 with a unique color. None of the bonus content was gameplay related, it was all stuff like documentaries, figurines, and soundtracks. Guns did, however, re-introduce a Metal Gear Online multiplayer mode, which was subsequently shut down in 2012. So you can't play that any longer.
Metal Gear Solid V: Ground Zeroes was basically a glorified demo, and as such didn't have any real bonus content associated with it. However, it itself unlocks some content in Metal Gear Solid V: The Phantom Pain via save data upload.
Metal Gear Solid V: The Phantom Pain had some cosmetic items made available to players who pre-ordered it (at least on Steam, I'm not sure about other platforms). You can upload your Ground Zeroes save data (again, at least with the Steam versions) and unlock some extra characters for use in your base operations in Phantom Pain. Presumably at some point the backend for that data exchange may go down, at which point this would stop working.
Similarly, Phantom Pain has an online mode, which launches in October. Given Konami's track record, you can expect this to eventually be shut down. Similarly MGSV's "forward operating base" game mode... which I don't know much about but sounds kind of like Clash of Clans-esque base raiding? is backed by servers on Konami's end and will eventually be sunset.
Metal Gear Acid didn't have any interesting extra content, but it's sequel, Metal Gear Acid 2, came with a physics stereoscopic lens add-on that might be difficult to obtain now, although you can probably easily find a suitable workaround.
Metal Gear Solid: Portable Ops had a pre-order package with some extra camouflage and such. The game had a peer-to-peer multiplayer mode, which still functions (as far as I am aware), although you'll need to find other players to actually play it. Metal Gear Solid: Portable Ops+ expanded the online mode but otherwise offered nothing new in the way of content you might now miss.
Metal Gear Solid: Peace Walker didn't have any bonus packages, but does have a multiplayer mode. As with Portable Ops, I believe this mode still functions, so all you'd need to experience it is friends.
Metal Gear Solid Touch is an iOS game, and as such can't have any kind of pre-order exclusive content. It was only release for select regions, though, so if you're not in those regions you cannot buy it.
Metal Gear Arcade is interesting, and not a game I'd heard of before researching this question. It was only out in Japan, so it's something you'll miss (potentially) in that sense. It was also basically an arcade version of MGS4's online mode, and consequently may not be running any longer. It appears that the game used head-tracking controls, which might have been fun.
Metal Gear Solid: Social Ops is another game that's only available on mobile platforms in Japan. It was a sort of mash-up of gameplay from other portable Metal Gear titles, and backed by servers that Konami shut down in 2013.
Finally, Metal Gear Rising: Revengeance had an assortment of physical bonus or collector's items, but nothing really gameplay affecting. There are versions of the game out there that include all of it's associated DLC.
So basically, the major content that you can expect to be missing out on by playing through the series today is either not gameplay-affecting in any major way, or was multiplayer in nature. And frankly, console online multiplayer being what it was in the age when the associated games were released... you aren't missing much.