I actually watch a lot of them with my daughter, because I'm not that picky about moderate violence, Hinduism, or bellybuttons.
Of course, they're very long and you have to have a kid who's willing to read subtitles. Here are some of my favorites to watch with a kid (she tends to like the fantasy themes the most):
Paheli -- a beautiful, lavish, and surprisingly feminist version of a Rajasthani fairytale, about a ghost (bhoot -- it doesn't translate exactly in English, more like a spirit) who falls in love with a neglected bride and takes her absent husband's place. When her husband returns, a dilemma is posed.
Seeta aur Geeta -- a Cinderella story in which the long-suffering heroine is saved, not by the prince, but by her own butt-kicking identical twin. Some fight scenes (very fakey, though, and no graphic violence) and a couple of drunk scenes.
Bhootnath -- a little boy movies into a "haunted mansion" with his mother (his dad is away working on a cruise ship) and is not all afraid of the resident ghost, who at first tries to scare him but then becomes his friend. He learns the ghost's sad backstory about being estranged from his family, and helps him resolve it and reunite the family. This one is really a terrific family movie -- I think it was intended for kids.
for grown-ups or older kids:
Hum Dil De Chuke Sanam -- So so pretty! And great songs. A very lavish romance about a love triangle. There's really nothing inappropriate for kids, I just think it might bore most of them. this might be my favorite Bollywood movie.
Kuch Kuch Hota Hai -- Another romance. The clothes in the whole first half of the movie, when our characters are wacky college students, are just horrible, and it's a little hyperactive -- but it succeeds because the leads, Kajol and Shahrukh, give truly wonderful performances and we end up deeply invested in their happiness. Actually, this one should be fine for children, I just haven't watched it with mine yet.
Company -- gritty, intelligent, well-made organized-crime drama. Not for the kiddies!
Sholay -- all-time classic, a "Curry Western" modeled on Sergio Leone with an all-star cast, great songs, and the biggest villain in Bollywood history.
Veer-Zaara -- Gorgeous romance about a love between a Pakistani girl and a Hindustani boy that ends in a great injustice, and how it is resolved decades later.
Jewel Thief - the last word in lavish '60s production design and hallucinatory dance numbers. Great stylish fun!
Asoka -- So sad, so beautiful. An historical epic about the midieval king who embraced Buddhism and promoted it in India, after a career of violence and conquest. Lots of battle scenes and intrigue, but a beautifully made movie with spectacular songs.
Om Shanti Om and Main Hoon Na -- two wonderful movies that both spoof and celebrate Bollywood conventions. Main Hoon Na is a wacked-out college comedy/action movie spoof, and Om Shanti Om is a reincarnation story about both the '60s and the '90s Hindi film industry -- they're both super fun. But it's better to have seen a few movies first, or you won't get a lot of the jokes! They're very referential to other movies and to movie cliches.