I'm a big fan of what are usually called "casual" computer games. Such games are typically designed to be accessible to a wide audience, don't require a lot of learning to play, and can be completed in a relatively small number of hours (most often 4-6, I'd guess.)
I compiled the following list of favorites for a friend who's just getting into them. I've been playing regularly for over two years now, and some of my older faves aren't as sophisticated as the best new games, particularly when it comes to graphics. I love 'em anyway.
(A lot of my little comments deal with how "dark" the game is. For perhaps a year, there's been a strong tendency for "hidden object games", as all but one of the below are, to be deeply suspenseful and creepy, even becoming almost horror. In my view, there's too much of this - but some of the games designed that way are really, really good games.)
Awakening: The Dreamless Castle
Lovely. Sequel "Awakening: Moonfell Wood" also very good
Dark Tales: Edgar Allan Poe's The Black Cat
Quite dark, quite good.
Drawn: The Painted Tower
One of the very best. Sequel "Drawn: Dark Flight" may be even better, but play this first.
Lovely, interesting twist on gameplay. "Enlightenus II" not -quite- as strong
Lost in Time: The Clockwork Tower
Fun, a couple interesting twists, a respite from the darkness.
This is one of the games that got me addicted. Sequels also good.
Mortimer Beckett and the Secrets of Spooky Manor
1st of 3, I like this one the most. Not sophisticated, but I've played it dozens of times.
Nightfall Mysteries: Curse of the Opera
This one's so dark, I haven't played the highly-regarded sequel. But very strong.
PuppetShow: Mystery of Joyville
Dark, but excellent: sequel, "Souls of the Innocent", also great
Snark Busters: Welcome to the Club
The Serpent of Isis
A bit dated, but one of my faves of all time. Sequel coming soon
The best "Match 3" game I've played