I've got several for this topic.
Mario series:
Come on! It's the game whose orginality made the gaming industry the way it is today! Even though the concept of the storyline might have been reused over and over in many other franchises (princess gets kidnapped, unlikely hero comes to rescue her, etc.), the things you do along the way are orginal. The enemies are a bit absurd, but very believable, and how you defeat them is believable too, since there's no magic needed (except when you shoot out fireballs and fly in the later Mario games, but that's beyond the point). The hero is a regular human that's a plumber too, which I think is very orignial!
Katamari Damacy:
I'm not sure if I spelt the name of that game right, since I don't actually own the game myself. From what I've seen though, it has to be one of the most original games ever. Whoever made this game the way it is probably has to have been on drugs. Either that or that person has a huge amount of imagination and creativity. Whoever came up with the concept for this game, I salute you.
Pikmin:
For the same reasons as Katamari. Again, I don't own this game myself, but I do remember reading in an EGM magazine in an interview with the creator of this game about 2-4 years back about how he came up with the idea of this game while staring at his backyard and gardens as ants were going along with their merry lives.
Rockman.EXE/Megaman Battle Network series:
Probably not one of the most liked series when compared to Mario and much of the other Rockman series, this series brings the concept of the internet to the point where it controls most aspects of every character's life in this game. And for those of you thinking 'Matrix', no, it's not like that. When you've got every single modern device connected to the internet, in an age where viruses are rampant and can cause destruction, in an age where crimes are now far from simple, total chaos can insue. The battle system is rather original, with you controlling whatever character you happen to be controlling at that time. It's turn-based battles on a real-time battlefield, as some might call it. I'm not going to go into the details as to how the battle system works, because it's going to take me forever to do so.