Kerbal Space Program is essentially NASA by trial and error. All the fun of building things and launching them into space, without the hassle of acquiring funding or the responsibility of having to return people to Earth safely.
The Kerbals are a race of little green humanoids who love space. More than anything else, they want to go to there. You can get them there by designing rockets and space planes of near-unlimited complexity (read: convolutedness), and testing them out. Some of your designs will succeed, and some will experience a "rapid unplanned vehicle disassembly." But that's half the fun.
Once you get the hang of getting things off the ground, you can really start to see how incredibly in-depth this game is. There is an entire solar system modeled here, with 7 planets and a bunch of moons orbiting them, giving you tons to do -- enough for hundreds of hours of play. As of this writing, I'm over 100 hours spent in-game, and the furthest I've gotten from Kerbin (the Earth-analog starting planet) is Eve, one of the nearest planets (and even then, I was forced to watch helplessly as the craft crashed into the surface, having spent all of its fuel on the voyage there).
The game's physics are -- while scaled down for difficulty's sake -- actually fairly realistic. I never realized how little I knew about the physics involved in orbits until I started figuring out how to save fuel during launch by focusing more on horizontal velocity. Before long, I was looking up how to do gravity assists to get to other planets, and looking up actual rocket science formulas, trying to understand the principles behind them in order to improve my designs.
The game is still in Alpha, and as such it's a little rough around the edges (the most obvious to me is that the surface of Kerbin is devoid of any kind of structures besides the space center), but new updates are coming out with decent regularity. Most recently added is the career mode, which starts you out only with a handful of parts, requiring you to perform experiments and generate reports around the solar system to gain "science" -- a currency you can use to unlock new part selections. The part limitations give a new kind of challenge, and obtaining science gives the game a more objective focus, which I found very refreshing -- especially just as sandbox mode was starting to lose some of its draw.
If designing and flying rockets, space planes and/or whatever ridiculous contraption you can think of sounds fun, it's a safe bet that you'll enjoy this game. Despite still being in alpha, it's already more than worth what I paid.