Any good brand of sport sandal; it is best to have a shoe with a heel strap, so that it con't fly off on coasters. You'll want something that can take getting wet, rather than sneakers which are miserable if they get soaked on a ride like Kali.
For kids, the Land's End water sandals are a nice value; also, if you shop at places like Sam's Club, right now they have some Eddie Bauer's at a very good price (actually made by Merrell). I have also sometimes found Khombu sandals at Marshalls; that's an excellent Canadian brand.
Tevas, Chacos, and Keens are great shoes, but a bit pricey, so I generally didn't buy them for my kids when they were young and growing through several sizes a year. My DH and DS are devoted Keens fans, I prefer Merrell or Clarks Privos, and DD prefers Merrells.
I would also advise buying a couple of sticks of Body Glide (made for runners) to use to lubricate any hot spots; Body Glide is water resistant, so it doesn't easily rinse off.
PS: For those who say that sneakers don't get soaking wet on Kali, I have to wonder if you've ever been on the ride. There is a foot bar about 10 inches off the floor of the raft that is supposed to keep your shoes dry, but it absolutely does NOT work for the majority of guests. Depending on the weight load of the raft, there are often situations where that bar will go underwater for 30 seconds or so. Most younger kids' feet can't reach the bar anyway, and their dangling feet are usually right in the path of the waves that wash over the side.
Besides that, one of the most fun activities for young kids are the splash fountains, and sneakers will definitely get soaked in those.