First IBM PC game? Quest for Glory, back when it was known as "Hero's Quest".

First game for a personal computer (the Commodore 64)? A bunch, including Crush, Crumble, 'N' Chomp, Jet Boot Jack, The Dragon's Playhouse, Treasure Island, Caveman Ugh-Lympics, Star Trek, and one of the old Infocom text adventures (but I can't recall which).