Allow me to nerd out a bit about video games. The following are gross simplifications, and I've done exactly zero study on this. In other words I'm blabbing, not researching.
In most games, you provide input to the system, and that input directly corresponds to motion by an avatar of some kind on a screen. Pac-Man moved up/down/right/left, Space Invader shot and moved around, and in Grand Theft Auto you can punch, shoot, run, drive, etc.
There's another kind of game, where the input to the system modifies the experience in different ways, rewarding you for providing the right inputs. For example, the trampoline gymnastics minigame in the Wii Olympics, you press a series of buttons in the order specified during a very short time. Get it right, and your avatar tumbles, flips, and performs a smoothly beautiful routine. The crowd applauds. Get it wrong, and you barely make it back on your feet to jump again, and the crowd registers its disapproval.
Rhythm games definitely fall into this latter category, and the most recent one to get in the public eye would have to be Guitar Hero. I played GH3 for the first time this weekend, and it's difficult to explain how fun it is. The gameplay is fairly simple to describe. Colored markers move towards you, and as they hit a "line" you must press a button corresponding to the marker's color while pressing another button to "strike." It feels very guitar-like -- you're holding down the strings with one hand while strumming with the other.
What makes the game so much fun is the feedback system. Play flawlessly, and you hear the exact song you think you are supposed to hear. Make a mistake, and a note is missed in the song, or worse, an incorrect sound is produced. So you're mentally rocking out to Metallica and instead of hearing what you want, you hear an awkward clanging sound. It throws you out of the groove and makes you flinch. Screw up a few times in a row, and the crowd turns on you, and the pressure grows. Get back on track, or lose the game.
It's a fun game to watch, because you're listening to music and watching the entertaining antics of the fictional band going on in the background as the player focuses solely on the colored dots. And it's a fun game to play, because in a very real way you are creating music by your actions, with immediate positive and negative feedback for every single button press.
I'm far from an expert on rhythm games, having only played Dance Dance Revolution a few times prior to this. But I can say, for me, Guitar Hero is much more fun than DDR. You are producing the music, not just controlling something that moves along with it. It's so much more satisfying when you win.
I can't imagine how much fun Rock Band is.