There have been so many great games over the years, I don't as yet feel I have time to say anything about most of them. Instead, I'll just put their images here. As with books, I'll try to have them more or less in the order that they came into my life.
My first game was Aldo's Adventures, a Donkey Kong clone for PC. My first favorite game was Scorched Earth, a 2D tank warfare game with a variety of weapons. Games that truly stand out to me, even among this list, are:
the Marathon trilogy (and fan-made scenarios like Rubicon, RED, and Phoenix).
Castle of Dr Brain, a quirky series of all kinds of puzzles that made learning fun. There were memory puzzles, jigsaws, logic puzzles, number squares, and more.
Morrowind, for getting me so addicted so quickly, that after only playing for a couple hours on a friend's xbox, I never stopped thinking about it even after 10 years.
Improbable Island, for making me laugh so hard I cry, on many occasions. (WARNING: F-bombs; also, it's text-based, which also isn't for everyone)
Zelda: LttP and OoT, for a certain magical quality I can't quite place my finger on.
Warlords Battlecry, for the extreme diversity of playstyles possible, both from variety of faction armies, and for the hero's class abilities and spells
Total Annihilation, for its realistic physics, and the fact it had both a navy and actual nukes (looking at you on both of those, StarCraft!)
Sunless Sea, for the bizarre and fascinating stories it has, and the strange and mysterious world they paint. London has been swallowed whole, and the survivors contend with everything from giant talking sea urchins to sapient mushrooms that love poetry