All right. Games. Let's take it in chronological order.
1st games I dealt with were for 8-bit processors. 8080 based computer PMD made in Czechoslovakia and run Manic Miner. It was very popular here. Some time afterwards my parent's bought my Atari XE800 hoping to develop my attitude to computers. However they made 2 mistakes. Atari XE800 was based on Motorola processor that dit not take off. At least not so much as ZX Spectrum or PMD line of computers. On the other hand Atari was more designed for playing games supporting colors and sounds.
The second mistake was - they had no idea how computers will attract me. I don't have a problem with that. They did ;-)

But let's have a look on list of games that I realy liked.

F29 Retaliator
Flight simulator. You select one of 2 planes, pick arms, take a mission. Simple, small, runs with (now) ridiculously low resources. Can be played across serial line by 2 players. Maker: Ocean.
A soldier runs in a maze trying to find an exit to next level shooting everything what moves. Endless hours of fun. You lean around your screen trying to see around the corner.
Next stage after Wolfenstain, with proper sound effects you get scared when you can hear the beasts breathing next to your ear. To explain how deep it draws you in, I'll tell you what happened in a dream to my co-player: I was running to a bus stop. The bus was just about to leave and I needed 100 yards. Damn, I'm not gonna make it. I should better press F8(quicksave). You know, just in case I don't make it. After weeks playing Doom, you'd open the door and jump aside in case somone is behind them ;-)
A bit worse than Doom with the same scenario and basically the same engine, just with different graphics. Nice but it wasn't so popular and it is not so much fun playing singleplayer.
Simillar to Doom but, you fly a space craft instead of running a soldier and the maze is 3D. Really 3D. Looping, screws everything is allowed. O god, how much time I spent with Descent. With my friends Palo, Vlado, JPI we often played till 2-3 a.m. I would give it a try anytime again. Unfortuntelly Vlado crashed into the ground of the airport in March 2003 with a small turbo plane and a copilot. Sigh.
Dune II
Dune I was advanture game based on Frank Herbert's novel Dune. I never really liked advantures, but Dune II was 1st RTS - real time strategy game. A good relax. Anytime.
Another real time strategy. This time networked. I wish I had time and peers to give it another try.

Current games are different. As one slashodotter said: they have better graphics, sound etc. etc. but they are not so much fun to play.

I'd like to try some current games such as Ultima Online, Unreal Tournament etc. but as far as I understand they are not for single-player. My internet connection is useless for games and they usually require lot of time. Can't afford that.