Cactus Game Design Message Boards

Little Big Planet and all the related games.
I think the Kingdom Hearts games are available on PlayStation Network by now, they do include cartoon violence so maybe read up a bit on them but overall they are very family friendly.
The Crash Bandicoot games are also on PSN, Crash is kind of the PlayStation version of Sonic I guess. All games rated E. Was probably my favorite series growing up.
There are Lego versions of nearly every pop culture movie series. Star Wars Harry Potter and the like.

Edit: and the PSN games are usually $15 or less. I have no idea what the original little big planet is down to.

The Final Fantasy and Elder Scrolls games, while some of my favorite, are not very family friendly. The rest I can't comment on since I've never played or heard of them.

I believe LEGO Star Wars: The Complete Saga is available for PS3 (it's basically LSW 1 and 2 combined into a single, refreshed game). LEGO Star Wars 3: The Close Wars is also on PS3 and I thoroughly enjoy it. Same with LEGO Lord of the Rings. I enjoy the LEGO Harry Potter games as well, but they are based on the movies/books and revolve around magic (replaced the Force from the LEGO SW games for manipulating objects/people in the world). LEGO Indiana Jones (LIJ) 1 is pretty good. LIJ2 is okay but suffers from horrible hub design (the overall world that you are running around in whenever you aren't in a specific mission). LIJ2 is a remake, just so you're aware, of LIJ1 with the addition of levels for the 4th movie.

Little Big Planet can be fun, though it quickly became boring for me personally as it is rather repetitive.

If you enjoy card games, Eye of Judgment (EoJ) is a fun game (especially if you have family members to play it with). EoJ requires the Playstation Eye camera, and it can be hard to find the starter pack anymore (has the game, a starter deck, the playmat, and the Eye camera), but if you can find it and manage to set it up (the camera can be spazzy with dim light) it's enjoyable. There's no gore or bad language that I can remember, though it's been a bit since I last played it (my apartment doesn't have both a flat surface large enough AND sufficient illumination in very many places).

If you enjoy puzzle games, I highly recommend Echochrome. It has puzzles based on perspective and point of view and it's thoroughly enjoyable. Available on the PlayStation Network store.

PM sent YMT. I forgot to put this in the PM, but if you do end up getting EoJ I'd love to play some matches against you or your family once you get acquainted with the game.