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You can't go wron with a giant invisible rabbit! This has been my favourite film since I first saw it about age 8 -forty years ago. I watched it recently with a couple of my god-daughters, aged 12 and 10, and they were interested but didn't really get it. I'll try with my own daughter soon (she's just 4 now). The great thing about it is that it works many levels simultaneously. There's the surface humour, a bit slapstick and increasingly surreal, exquisitely delivered by Jimmy Stewart and the rest of the cast. But with emotional depths and resonances to each scene. I find something new every time I watch it.
I'll second the vote for Arsenic and Old Lace, for older kids anyway. My second favourite movie of all time! Bringing Up baby is no.3, but it's already on the list.
On the Muppet Question, my vote must go to Muppet Treasure Island. My daughter loves it, as do her mum and me. Muppet pirates! Tim Curry! singing skulls! A duelling frog! C'mon, it's the best!