Wow, some good lists by owl, esuna, and satanic. Just packed up my big 6 foot stack of game boxes so I'll have to break those out later and find some good ones. Maybe even power up my 486 if I'd be arsed to do so. Here's a few, they may not be "influencial" but they're classics nonetheless:
Oregon Trail
Battle Chess
SimCity 2000
SimFarm (seriously)
F19 Stealth Fighter (Dunno if its based on another game's engine, but it sure was the best flight sim game from the 80's I ever played)
Dungeon Siege (yes, I know its a Diablo rip-off, but it was done hella-good)
Dungeon Keeper I & II
Urban Assault (<------ !!!!!!!)
Well that wasn't very long, esuna stole all the good ones!
Off-Topic: Holy hell satanic, Pikmin 2 was released? I feel so out of the loop! /me runs to the local rental store