1. Age of Empires 2 (RTStrategy/LAN)

2. Half-Life 2 (FPS/Puzzle/Story)

3. Skyrim (RPG)

4. Quake 2 (FPS/LAN)

5. One Must Fall 2097 (Fighter)

It's hard to narrow down, but these are some of the more fundamental ones growing up, with depth, but also fairly accessible.

Single player, multiplayer, co-op, moddable.