Super Mario 64 is the clear winner for me here. I was so blown away by it, I spent a good chunk of time just jumping around the castle's front area before I actually started the game. I also remember my friend opening that 9-star door and we both thought we reached the end with Peach right there in sight, but nope. We totally got fooled. Great game.
Other standouts:
Kirby Super Star - Incredibly fun to co-op through and I like the less 'cutesy' approach they went with.
Pilot Wings 64 - I loved to just fly around the evening sky. Oh how I wish this would get a VC release somehow
C&C Red Alert - Didn't play the PC version until wayyy later. The construction animation that the PS1 version lacked were so rad
Civilization 2 - Good sequel. The windows version is so light that I booted it up on my crappy laptop just a couple of years ago for some CIV on the go.
Settlers 2 - Didn't know what I was doing, but building a town of random structures was still a lot of fun! (until materials ran out)
Terranigma - Already talked about it in the 1995 thread, but it's one of the SNES best so I'm mentioning it again.
Warcraft II: BtDP - First RTS game I bought for myself. Loved it, sad I never got online multiplayer to work on it.
Wave Race 64 - When a friend bought it, I couldn't get into it. Then I borrowed it and got REALLY into it (but then said friend thought it sucked, lol)