In no particular order...
Final Fantasy VI (US3) - For the story, variety of well developed and unique characters, and for being the only Final Fantasy game where the antagonist actually wins for a few years. The final Kefka battle is some of the best 16bit artwork ever.
Final Fantasy VII - Unique storyline, great character development, beautiful cutscenes, and for being my first exposure to RPGs.
Street Fighter 2 - Played it in the arcades in my early teens, played it on the SNES in high school and college, played it on the PS2 when it was released in a Capcom GH collection, and purchased it on the VC for my Wii. Apparently I just can't get enough of this game.
Mario Kart Double Dash - Just plain fun. Especially with friends.
Diablo 2 - Spent a ridiculous amount of time on this game. Diablo 1 was very good also, but the level design, extra classes, and loot of Diablo 2 kept me hooked for untold amounts of time.
Titan Quest with Immortal Throne Expansion - Still playing this with my 4.5year old son. He loves it and I love playing it with him.
Total Annihilation with Core Contingency and Battle Tactics Expansions - I upgraded my computer specifically for this game years ago. Still break it out on occasion and play it.
Super Mario Bros. 3 - Glad to have this on VC for my Wii. Most unique SMB game IMHO, and was years ahead of its time when it was first released.
Super Mario Galaxy (even my "non-gamer" friends played this like people possessed to get all 120 stars). The musical score is awesome too. Not sure if I'll play this throughout the years, but the experience was wonderful.
Bioshock - Its creepy and spooky. It scared me witless and made Rapture come alive. The artwork, atmosphere, gameplay, and story make it one of my all time favorite FPS.
There, I limited it to ten.