Well, might as well throw my selections in here.
Chrono Trigger (SNES). Always felt it was a great RPG. Wonderful story, a lot of characters without having too many (so I stopped caring about any of them). I loved how the combat worked later in the game with concepts like the dual-tech and triple-tech moves, gave the battles different ways of being played out (ignoring the "Attacks everything on screen" techs). Also having access to multiple different ending with the New Game+ option was really great since it was always fun to see "Now that I've changed X in the games time line, what does the ending look like now?"
Blood (PC). Standard first person shooter, but with lots of over the top gore and dark humor. Also had quite a few new ideas for games that later became standards (like alternative firing modes for weapons). Its a nice break away from the military/space marine themes that are in just about EVERY other FPS. Also some of the weapons really interesting and fun to use, like the Flare Gun that let you set enemies on fire, Telsa Cannon that could shock and hold the enemies still, a voodoo doll (with a finishing move of a crotch stab) all the way to the Soul Leech that if it ran out of ammo it would start using your health to fuel it. Had a great multiplayer map as well, a soccer field that when you killed someone and their head popped off you could kick it into the net for a field goal.
Strife (PC). While another FPS, this one wasn't all about "Shoot first, ask questions later" and it also had a story line. In fact, you couldn't "Shoot first, ask questions later" because it would cause the local police to start warping in and trying to kill you (and shop merchants would close up while the alarms were off). One of the things that also helped set it apart from other FPS's of the time was that it had 3 endings (one was from if you died on the final boss). You could also obtain extra ammo and health by purchasing them from the local merchant. While it might not compare to todays games, it was quite amazing in 1996.
Guild Wars (PC). What can I say? Its a great MMO that had a real story that you could follow and was interesting. Its usage of only allowing you to choose 8 skills at a time made you have to sometimes rethink how you were going to do some of the quests/missions allowed it to be less of a repeating skill usage that is found in most other MMOs. Another nice function was the removal of a huge level grind (max level 20 and that wasn't hard to hit) also allowed it to be less grinding and more skill based (learning what worked great with what instead of just being a higher level/better geared).
And finally, Starcraft (PC). A RTS that isn't of 2+ races that aren't carbon copies of each other with one or two differences. It had a good story, lots of mission maps to do and a great as well as free multiplayer option that always made sure it would be fun. And the multiplayer option is what I feel made Starcraft such a great game. Its inclusion of an easy to use Map Creation program really helped make the game always stay fun, and it even allowed you to make scripts on the maps so it wasn't always the same RTS game on different maps, but sometimes make it a whole different game (like the Zergling Rush maps, ect....)
**Edited to make it a little clearer to read**