The first game I remember playing was the DOS version of Sokoban published by Spectrum Holobyte, and I would have played it on my father's 286 type computer around 1989 or 1990, I imagine.
Other games of that time I remember having at home were Battle Chess, Blockout and Test Drive Lotus Esprit.
All of them were, I felt, graphical powerhouses, with photorealistic impressions and decent animations. Battle Chess ended up being quite a nice toy to have (being that I have always been a very poor chess player) just to try and see all the different animations. The CPU also took ages to move (afair over 2 to 5 minutes to move), which made the impression that there was some little man inside the machine trying to think of his next move before pushing the pieces. The "wait" icon was a miniature of Rodin's "The Thinker", the kind of cultured detail you hardly see in games these days.
An uncle also had a Macintosh which, even at around 1990 still looked quite slick in black and white. Most memorable was Stuntcopter. It also had a few parlour/board games like Wheel of Fortune, Hangman, Iago and Risk which were interesting takes on the board games, much like Solitaire when we finally got Windows 3.1 at home.
First console game was Sonic the Hedgehog that a neighbour who was my age had, as his father had got him a Mega Drive. Not much later I got a Master System II which had Alex Kidd in Miracle World.