How could you not feel for the characters? Lilo was an "outcast", didn't have any friends, just lost her family...her sister was struggling with everything and the one thing she wanted more than anything...(her little sister) was falling out of her reach. Lilo just wanted one thing in her life...a friend...someone she could rely on...someone she could talk to...someone she could relate to...to help her cope with the loss of her parents. Then comes Stitch...who she falls in love with right away. Stitch also didn't have any "friends"...everyone he knew wanted him "gone." Stitch grew to "feel" for Lilo and wanted the same things that Lilo wanted..."SOMEONE." Sure, Stitch is a little "rough around the edges" but wouldn't you be if you had nothing? No reason in life...no reason to love...no reason to exist. Lilo was a little rough around the edges too...because she only had a sister...who she thought didn't want her because she was too much of a burden on her.
Throughout the movie you see that Lilo realizes that her life isn't all bad once Stitch comes into her life. Stitch truly has nothing...not even a name! Lilo became the "parent" who teaches Stitch that there is a reason to live, laugh, and love.
I think the characters appeal to a lot of people because everybody (at one point in their life) has been down in the dumps...and needs a "figure" to relate to...Stitch and Lilo are those figures. Kids love Stitch because (boys like him because he looks like a monster and girls like him because he's "cute" at the same time :lol: ) he gets into trouble a lot!
I dunno...that's my take on it