Although based on the upcoming movie
Lilo and Stitch, the game actually takes place before the movie begins. In the beginning, you are charged with collecting DNA for Jumba's experiments. Eventually, the Government (I think that's who it was, the game doesn't explain the story very well) finds out about Jumba's 'genetic abominations' and you're soon on the run trying to activate a transporter (I think, again, the game doesn't do a good job at explaining the story).
At its core, Stitch is a pure action platformer. He jumps, runs, climbs and shoots his way through world after world collecting DNA. Overall, the game is fun but it fails to overcome many of the pitfalls that plague other platformers. As I mentioned before, the camera system is very hard to use and makes certain situations harder than they need to be. In order to try to break up the game, certain areas require you to either jetpack or swing (via grappling hook) through them. These areas are fun but leave a lot of be desired. Some of the thinking that went into these areas also dumbfounded me. For example, in order to recharge your jetpack you have to fly through a green ring. The problem is that once you fly through one ring, you have to fly through a series of rings or you die. To make things worse, the game never gives you any reason why you die - you're just expected to accept it and move on. I also found it interesting that these sequences are so over-used later in the game, that it becomes monotonous.
Scattered throughout the game's worlds are movie reels. Sometimes these are hidden in out of the way places and other times they are gained by chasing down 'Space Squids'. Collecting reels allows you to unlock clips from the movie as well as some very funny 'Inter-Stitch-als' (or trailers) for the film (I particularly liked the Aladdin one). I definitely do not recommend unlocking clips until after you've seen the movie because once they are all unlocked, you practically have a DVD of the entire movie.