Aww, I very nearly was in a TMNT roleplay game once upon a time, but the guy who was going to GM it moved away suddenly. (same GM that almost ran a Night Life campaign which I would have also liked to try, but everyone else wanted to play D&D instead)
Dungeons and Dragons is what got me started on roleplaying games waaay back in the day. An old friend introduced me to it when I was in 2nd grade round abouts, and then I learned that my dad had some old books of his own laying around.
Advanced Dungeons and Dragons 2nd edition is the first RPG that I went out and bought myself, and that one lasted for quite a while. My friends and I used to make up all sorts of crazy worlds, campaigns and things. I don't think I could count how many different little games we tried with that one.
D&D 3rd edition I didn't really like this one very much, but I did play several games using it. Planescape, Legend of the 5 Rings, forgotten realms, tomb of horrors, and one horribly ill fated epic campaign that got people arguing over a single round of combat for hours. I didn't like how everything about your character had to be planned out in advance, especially with how rare feats were, and my friends were much better at cheesing the system than I was.
Shadowrun 3rd Edition I think this was probably one of first non-D&D games I played. It was very fun and lasted for quite a while, but nobody could ever figure out the matrix combat rules, and vehicle combat... we had a house rule. Once three shots had been fired, everyone just pulled over and fought each other on foot.
Shadowrun 4th Edition is one we still play just about every other thursday night over Mumble. It got a lot of things right, and made a few other things worse, but thats what house rules are for. All in all, a relatively flexible system.
Eclipse Phase is a game that I really wish I had more of a chance to play. Only ever got to play a few sessions of it here and there. Its a perfect setting for facing horrors from outer space, though some of the setting elements are a bit silly, it does what it needs to do. (The whole ability to switch bodies in the setting is great for the GM because it means you can kill your players and not feel guilty about it, they can always re-download from a backup.)
West End's Starwars (D6 version) was great. Its what finally sold me on game systems that didn't use character levels. We played an almost year long campaign that sadly ended before its conclusion. Plenty of great and memorable moments though.
My own homemade system #1 got a few games under its belt with my friends. Turns out, I liked the Starwars campaign that I was in so much, that I converted its rules into a Tolkienesque fantasy setting, along with a healthy set of house rules tacked on. Eventually I went and diverged so much with house rules that none of the original rules remained and I was left with my own homemade system #2 that I'm still poking at to this day.
Scion: Demi-god was a neat little game that I played a short campaign of a while back. It was a neat setting, but I think it probably would have been better at a lower powerlevel. It seems like once you get into demi-god range, you either succeed because you have so many automatic successes that nobody else can stand a chance, or you fail horribly.
Nobilis is a strange and beautiful RPG that is entirely narrative based. Your characters have stats, but there is no dice rolling whatsoever. Conflict is resolved by how badly you want to succeed, and thus, how much you're willing to give up to make it happen. Played a short game of that before our GM moved away, and it was pretty interesting.
Dogs in the Vineyard is a very cool little indie RPG that focuses on conversational conflict and relationships. Its sort of an old western with demons and you have to go around and root them out of various settlements. Conflict is decided by betting dice against your opponent. (If you can match your opponents bet with two dice, you succeed, if you need to use three or more, you take the blow, if you can't match it at all you lose the conflict.) I played one campaign of that and GM'd one where I switched out the setting for a steampunk setting.
GURPs is something I've played a few times here and there. One was a superheroes campaign, one was random passersby on the street that got sucked into the fairy realm only to find that victorian age Britons had gotten stuck there ages ago and were still trying to conquer it in the name of the queen, and just recently some friends of mine have been putting together a time travelling campaign where I'm planning to play a sentient velociraptor who can cast magic (and is in no small part based off of Twilight Sparkle's personality) The system itself can be very restricting, in spite of how many options it presents you.
In Nomine is a neat little game that I ran recently at the request of my friends. Angels vs demons and all that sort of thing. Lasted over a year which probably makes it one of my longest running campaigns ever. First one I actually concluded before someone moved away or something too. Rules were a little bit spotty, but its nothing a little creativity can't fix.
Vampire: The Masquerade was fun, I played in a medium length campaign of that once. It was set in the age of Jack the Ripper and I was a Malkavian who's derangement was that he heard all of the OOC chatter around the table as voices in his head, but whenever I talked back, it was in character.
Exalted I really wanted to play Lunars or Sidereals, but I've only ever played Solars. (And I'm not very good at character creation) However, it was pretty fun regardless of the fact that my character was very underpowered compared to my team mates. I made up for it by being clever and thinking of things the GM didn't expect.