I've had the demo version of Papa Stacker on my Droid for quite a while now. The game has a really nice demo that lets you play through the first 9 levels. The premise is simple... you're given a sequence of shapes (squares, circles, bars...) of various sizes displayed along the top of the screen and you have to stack them up in a stable structure (i.e. so that none of the pieces falls off of the structure) by touching and dragging on your Android's touch screen. The game ramps up in dificulty nicely. The shapes have cute little animated faces that show expressions of uncertainty or satisfaction based on your structure's stability and the cartoonish sounds make me think Flinstones.
My only real criticism of this puzzle game is how much of each level is thought versus trial and error. Yet, regardless I keep coming back for more doing a level or two here and there and it seems as I get deeper into the game it is making the transition from trial and error to thinking.
This game has been around for a long time and I'm impressed with how it keeps calling me back to play another level. I haven't done any marathon gaming sessions with it, but I'd rather have a game where I play a little here and there versus finishing it off in a day. The game includes 40 levels and has a level editor and, so far about 50 more community created levels. In a nutshell this game is a great, casual puzzler... give it a try!