One of my all-time favourites is "A Series of Unfortunate Events" - based on the novels with the same title. It's a logic game - all three featuring in this post actually are.
"Inspector Parker" works mostly like "A Series of Unfortunate Events". You have a couple of statements and with their help you have to work out where suspects, victims and so on where at the time of the crime to find out who did it and how (or, in the case of "A Series of Unfortunate Events" what happened to the orphans that time). It gets more and more difficult with time, of course (the first picture shows level two or three of the game, the second picture level 8 of the other).
"BeTrapped" on the other hand had a post to its own, a couple of months back. It's a bit like the Windows mine-sweeper. There's a couple of traps in each room and they have to be removed before Inspector Parker (featuring in this game as the main character while he's only the mentor in "Inspector Parker") can try to find out who's planting them and why. During the game, a couple of people are murdered and strange things happen. In the end, there's the usual gathering of the (surviving) suspects and the great solution - which the player has to provide. This way the game works on two levels: first, find the traps, and second, find the criminal. Even after the first or second time, the game still is fun to play, which is why I still play it every now and then, although it was the first.
I still like those games a lot, especially as they don't require a CD to run and can be played in windowed mode, allowing me to play them for a couple of minutes while working at other things.