I've gotten a lot of mileage out of the old TSR Marvel Super-heroes over the years. Yeah, this one's an antique, and it has huge limitations, but they did some really clever things with using abilities in unusual ways. Made for some imaginative gameplay, and I still pull it out from time to time.
The old World of Darkness system worked well for my group too. We're especially fond of Mage (again, a very versatile system).
I never got around to putting a Nobilis game together, but I really like the system here. It's another open ended system, where players can literally do anything, and it's diceless as well. Loads of potential, but a steep learning curve.
I'm not a huge fan of D&D, and most of the reasons are built into every generation of the system. Alignment's probably my biggest bugbear. Definable, objective Good and Evil really get in the way of my storytelling and roleplaying, and the mechanic doesn't lift out easily, so it can't be ignored.
D&D's the system I started on, but I haven't played since Reagan was in office. (Fine, it was AD&D, if you want to get all technical. Satisfied?) One of my group recently convinced me to give it another go, and I'll be starting a 3.5 campaign in the next few weeks, so we'll see if I can make it work for me.
Anima: Beyond Fantasy currently my favorite for fantasy setting; it has a great deal of detail for various supernatural abilities, and it combines aspects of level systems like DnD(you gain certain things with every level, guaranteed) with the freedom of point-buy games(you can develop your abilities however you see fit) with the interesting effect that if you're playing as a class that specializes in a particular ability, it'll be easier for you to develop that ability than any other class.(Though if they met the requirements, they're certainly more than welcome to do so.)
The drawback is that all the detail gives it a very steep learning curve. Additionally, if somebody decides they want every ability, they're not likely to be good at anything they do, or somebody who focuses on one ability will ALWAYS outclass the person who focuses on multiple abilities. (Though, this should be obvious, some friends of mine have felt in necessary to decry this phenomenon as one of the reasons Anima is a terrible game.)
Another one worth mentioning is the D6 System from the old West End Star Wars game. It's straight forward, versatile, and gives the players the ability to stack the deck when they really need to, which makes for good storytelling (nothing worse than uncooperative dice in a big climactic scene.) After Star Wars moved over to WotC, D6 became an open system, meaning it's yours for free. They've taken a generic approach, with core books for space opera, fantasy, and modern adventuring. Well worth a look.
I can second the West End Games sentiment Henry has; I played both their Star Wars game and their Ghost Busters game. While the two games from WEG I've played had some fairly different mechanics(Ghost Busters is much simpler than Star Wars), the core mechanics remained pretty much the same: roll d6 equal to your stat/skill, with at least one die in the pool being designated as special. Whenever the special die Rolls a 6, something happens: in Ghostbusters, it was always something bad, while in Star Wars it was simply something unexpected.
I like Pathfinder the best because it is the system I am most familiar with, I've briefly played Mutants & Masterminds, I've played Second Edition for a little while, and I've played games for Firefly and for Star Wars. But I'll play whatever the DM and the rest of my group want to play, since I am really there just to hang out with them.
So far, I've only ever played D&D. I've run 4e games, and I'm currently playing 3.5 online over at In the Time of Heros. I've also been reading the D&D Next Playtest documents.
So far, I prefer 4e over 3.5, but form what I've read in Next has me excited.
I'm also backing the Fate Core Kickstarter. I'm Liking this as well. Much more RP based, and very collaborative.