We don't normally link to advergames... But we're willing to make an exception for Junkbot, because we like it a lot.
Junkbot is a robot who works in a factory. His job is to empty garbage cans. Unfortunately, his programmers aren't too smart, and his pathing algorithms are dumb. He walks left-to-right until he hits an obstacle, then turns around and walks in the other direction. This would be okay, except that in most levels, something prevents him from getting to the garbage can. Your job is to build him a path--using Lego bricks (ah, the advertiser).
Okay. Except that each time you pick up and move a brick, you use up one of your allowed 'moves' for this level, so you have to figure out how to get Junkbot where he needs to go in the minimum allowed moves. And for bonus points, you can try to get him there optimally, meeting an even more stringent criterion.
Naturally, as time goes on, things get more complicated; dripping water will short Junkbot out, but you can build a shield for him with Lego bricks. Or updrafts will blow him up to another level, but he'll hang there unless there's some way for him to walk on further. And so on.
Junkbot was created by the folks at GameLab, who have created best-selling casual games like Diner Dash and IGF-award winning titles like BLiX. Junkbot shows what they can do when working in a more conventional, arcade-y mode--aiming to create games that actual gamers like.
Will it revolutionlize your view of the possible in the ars ludorum? No. But Junkbot is excellent for what it is, a charming puzzle game that poses real intellectual challenges. And it's free, and who can complain about that?