I'm not even sure I can narrow it down to one favorite per genre.

Strategy

Lords of the Realm II was a turn-based medieval kingdom simulator with real-time battles and sieges. I never played it online, and the AI was sufficiently predictable to be defeated with some practice, but it was a solid game.

First-Person Shooter

Descent might be more described as a flight sim, but it's more of an FPS with flight mechanics, if that makes sense. Anyway. A DOS classic that eventually even saw a PS1 port.

Racing

Most people seem to love Mario Kart, and that series is good, but my vote will always be for Crash Team Racing as my favorite kart game.

Puzzle

Portal. Yes, Portal 2 was better by every measure, but the original laid the groundwork.

Platformer

So many classics, but Ratchet & Clank is probably my favorote of the 3D games, with honorable mention to Jak and Daxter, while Duke Nukem 2 might be my 2D choice.

RPG

This is even harder to just consider candidates. So many good Final Fantasy games. Especially FFVI. the Fallout games are great. The Elder Scrolls games are great. The Witcher. Dragon Age. I can't choose!