I've been a fan of Amanita Design ever since discovering their first Flash game, "Samorost". They make point-and-click adventure games, featuring quirky characters, hand-drawn art, and ethereal sound effects. Each game gets better than the last, and Machinarium is definitely their best game yet.
I'd describe this game as a sort of Steampunk Myst: it's a Myst-like adventure game set in a somewhat run-down old city populated by robots. I'm also reminded a little of Wall-E, especially by the opening scene where the flying junk-ship swoops in and dumps the game's main robot character onto the junk heap.

You play the game by helping the robot find his way through the city. Along the way you'll learn why he's there (via his thought-bubbles/daydreams). Each level or screen in the game usually has a puzzle to be solved. Some puzzles are easy, some are difficult, and some are games-within-a-game. If you get stuck, there's a help book in the top right corner with the solution for that level... but you'll have to play a little mini-game to unlock the book.
If you idle a while, the robot will cross his arms and tap his foot impatiently. :) He also has several other "bored robot" mannerisms that are quite cute.
It's an incredibly artistic game. The graphics are all hand-drawn; there's no 3d here. The game also has its own full soundtrack, with music that really evokes the feeling and atmosphere for each level. In fact, as with some great movies, the soundtrack is a character of its own, an essential part of what makes this game so great.
Screenshots don't do the game justice, so I won't post any; instead I'll just recommend the Demo.
Machinarium is a delightful game. I haven't played many games that brought me joy, but this one definitely has. Big thanks to the folks at Amanita for creating such a fun game!