Hi, just wondering if you can recommend the games for the more old part of population to play.
See this as an alternative to gardening
Apart from card games, minesweeper, tetris, sokoban and so on 
SIMs are out of interest, RPG, shooters and massive multiplayers too.
No multiplayer will be perfectly OK.
Limitations:
- Half of hour maximum for a single session.
- Intuitive learning or forgiving for non-gamer.
- Something beyond raising virtual bonsai and moving furniture on a floor plan.
Just curious.
I already asked the heavy gamers in the family, if something exists for a people like me.
They said "Nothing at all" 
Well it depends on what system you are wanting to game on. If you are into the hand held market, for instance something like the Nintendo DS might be right up your alley. Games that I could see an older person playing would be Meteos, New Super Mario Bros, Mario Kart, Professor Layton and The Curious Village, Brain Age, and I'm sure a lot more. Anyway some specifics on what kind of system you are looking to find games for would really help me out! I own many games for many systems, so let me know what you have, and I will do my best to find you some games 
Desktop PC with Windows. Fairly good, but it falls 5yrs or so behind the modern requirements.
As I said, I have gamers in the family, and as soon as they improve their PC, I can use the parts left for improving mine.
I'll take a closer look at the game names you provided, thank you!
Well playing on a desktop changes things a little bit for me! I am not a hardcore computer gamer...However I do have a few suggestions: Puzzle Quest (This game is a puzzle game with RPG elements to it. I know you said RPGs were not up your alley, but I figured maybe you would give it a shot because you like Tetris (I think...)), World of Goo (This game is super fun. You really should start playing it like now haha), and definitely look into Audiosurf (Every .mp3 file is a new track! Super fun, and many different ways to play). All of the above games are below $20, and are pretty flippin fun. Audiosurf may or may not be available only on Steam (game download service), but you should download Steam and check out some of the other indie games on there.
Links:
Puzzle Quest:
http://www.reflexive.com/PuzzleQuest.html?RSS=1
World of Goo:
http://2dboy.com/games.php
Audiosurf:
http://store.steampowered.com/app/12900/ Most kind of you, I appreciate your help!
Virtua Cop2
good for their reflexes also
Age isn't always a restriction.
My grandma (68 years) has finished all Harry Potter games on her PC with max scores. 
That's awesome! I've only played the fifth one all the way through. I really want to play the sixth one as well. Right now I am running through Drake's Fortune, which is super amazing. Another great game is Braid. I believe it is for PC, but it could be 360 exclusive. If it's on PC, check it out!
Get a Wii and play Wii Sports or Wii Sports Resort. Those a games that you can pop in and out off really fast, and get you in motion. They aren't so great by yourself, but they are if you have family around.
Peggle. Though it's a game where you may find yourself playing for longer than you intended.
If you own a DS, the Ace Attorney series is great fun. It's a thinking-oriented, part-detective, part-courtroom drama game. It sounds odd, but the story has great appeal, the cases are fun to solve, there's a great sense of achievement once you've figured it out and the characters and dialog... absolute genius.
It's a game with a sense of humour, and it never puts you under any sort of pressure to do things quickly, giving you as much time as you need to think. So it doesn't matter if your reactions aren't as fast as they once were: as long as your brain is still in working order it's entirely possible to complete the game. 
