Two of a Kind (link on the right-hand side) is a nice light adventure with two playable characters with their own unique (and extraordinary) abilities.
Five Magical Amulets is a fairy tale style story which has won much critical acclaim and awards. (I must admit to being involved with this one. I proofread and beta-tested the English version)
The games of Yahtzee are always something I've enjoyed. 5 days a stranger and 7 days a skeptic are horror stories (7 days is a sequel. 5 days should be played first) The trials of Odysseus Kent and The Rob Blanc trilogy are humorous games. Adventures in the Galaxy of Fantabulous Wonderment has some elements of a trading game in an adventure setting. There are arcade style sequences in this one so you might want to avoid it if you don't want action. 1213 is a platformer.
Ben Jordan is a series of games about a paranormal investigator. I'd say the first and second ones could have used a bit more polish but from case 3 onwards the series has really hit its stride. I'm really looking forward to the release of episode 5. I'd recommend playing the earlier ones for backstory if nothing else.
Hopefully that's enough to get you started. No doubt other recommendations will be along shortly.
