The Man with the Invisible Trousers
There's two quirks about this case, though. First off, James' boss spent his entire life in one room. Realism aside, this means that it had to be an inside job... one of the members of the detective team had to have been the murderer. To solve the case, James has to make it through a gauntlet of spike-filled levels. Move with the [arrow] keys and jump with the [spacebar]. Your progress is saved automatically, so you can continue from the last level you finished. Every few levels, James talks to the other detectives and learns a little more about who might have done the despicable deed. This, however, is complicated by the second quirk. James is either wearing the titular invisible trousers or simply has no legs, so he reacts to gravity and curved surfaces in a very unusual way. Walking on a curve tilts James to match the curve, while walking off a corner causes gravity to act on James as if he was being pulled "down" relative to himself.
You can only finish a level by leaving through a door, but to open the door James has to be standing upright. This means that most levels consist of trying to manipulate James so you can both end up at the door and be standing the right way to open it. Be prepared to swear just like a film noir detective as you try make this happen, though typically the levels are short enough that having to restart isn't a big problem.
The Man in the Invisible Trousers features a classy, minimalist graphical style and some of the best jazz music in Flash gaming. It's also got a randomized ending; each time you play the killer will vary, though that might not be enough to get most players to go through the whole game multiple times. There's not much to say beyond that; there's one core gameplay concept here and it's done effectively and stylishly. It's worth a look for puzzle fans with a love of jazz and twenty minutes to spare.