How old to enjoy Disney?

We went to Disney World when I was 10, brother 8, sister 6. The trip was really good and my grandmother was with us, so 1 adult per child. I have a bad memory for the past, but I do remember some parts. I think my brother and sister remember it better than me even though they were younger. It was at Disney World when I finally got my parents to understand I needed glasses!!! (missed the table putting down my drink, apparently) We also got to go to a character breakfast and got some stuffed Plutos signed by the characters, which was fun.

If you're looking for fun, I'd say late 3 or early 4 as minimum, remembering it well, 10?

I went for the first time when I was in high school! And it was great, but I was more detached than I think a younger child would be. I've gone back a couple times as a uni student and an adult, and it's still fun.

I would second the recommendation to go sometime other than summer. Our first trip was in March and it was cool and drizzly--perfect, and far less crowded! The heat gets pretty miserable in summer.

ETA: I'm talking about Disneyland, not Disneyworld.