I know you're asking for people who like it, but I wanted to talk about an alternative reason that I didn't enjoy it. Many people just don't like the attraction because it's too scary or claustrophobic or a number of other things. However, there is a separate, more glaring reason that I really don't like the attraction.
I am a huge Stitch fan- it's one of my favorite movies in general let alone Disney. I hate that the attraction is focused on Stitch's untamed alien form. That isn't what most of the movie (or sequels/TV show) is about, and it's certainly not the reason many people love the character. There are so many things that could be done with the franchise that don't involve that part of his character. I don't understand why they chose to go with that, other than the fact that they were replacing Alien.
This isn't everyone's opinion though. As others have said, many Stitch fans enjoy the attraction. For example, my sister's (age 20) absolute favorite character is Stitch. She even has a Stitch doll that she brings to the parks to take photos with as a kind of memento of her trips. She loves the attraction and it's a can't miss for her. So it's different for everyone.
It's really a hit or miss. However, as others have mentioned, it's really a only a "hit" for Stitch fans (and only some Stitch fans at that). If your family aren't overly enamored of Stitch, they may not be as willing to endure the problematic attributes of the attraction.