Sport Sandals
Sport sandals are basically flip flops with straps. These straps, which usually go around your ankle and over your foot, secure the sandal in place so you don't lose it if the boat tips and you fall in the water. Sport sandals work in summer when you don't have to worry about keeping your feet warm. They don't offer any toe protection, though, so they might not be the right choice for rocky rivers, where there's a chance you will hit your foot against the rocks if you fall in the water.
Water Shoes
Water shoes or water booties are usually made of neoprene, a flexible material similar to the one used to make wetsuits for scuba divers. Water shoes are not meant to keep your feet dry, but they will retain some warmth and they also offer drainage, so the water doesn't stay against your skin and puddle inside the shoe.
Long Booties
Water shoes come in different types and sizes. Some reach the ankle, just like sneakers would, while others are a few inches higher or extend to just under the knee. Longer ones are best to protect your skin against the elements, including wind and cold. Some knee-high booties are waterproof and designed for cold weather.
Shoes
You could wear plain sneakers when kayaking. If you do, choose a pair with ventilation holes, so the water can drain out. Looks for shoes with mesh panels and made with synthetic materials, rather than leather. Choose shoes that have straps that snap closed tightly. Shoelaces are not the best option, since they can get tangled in the boat or in the rocks or branches if you fall out of the boat.