What Are The Best iPhone apps to keep a toddler amused in an 'emergency'?
Preferably free - kids shows / films from iTunes are an obvious one.
Bubble Wrap
Bubbles. Works great on iPad also. It's important for toddler software to be ad free, since they will click on links.
There is a free limited version of Sound Touch but personally I think the full version is well worth the few bucks it costs.
My daughter went through an obsession with Monkey Preschool Lunchbox. I can vouch that it's highly educational, too. She became much better at counting (after about 2 weeks, she no longer needed to count out groups of 10, she could just look at a collection and say "there are 8 bananas.").
Not free, but the various Dr. Seuss apps are great, as they will read the book out loud at the child's pace. I also always have "Animal Sounds" at the ready.
For free, my daughter spends more time browsing photos of herself, family, and friends (in that order) than doing anything else. Go figure.
Oh, we get a lot of mileage out of (pirated) episodes of Dora the Explorer.