CRT and the dinner shows (Hoop de Doo, Spirit of Aloha, and I believe Mickey's Backyard Barbecue at FW) require payment in full at the time of booking (note- full payment, not a deposit) with a credit card. A few other reservations - Akershus and California Grill come to mind - require a credit card guarantee, meaning they will take your credit card number and charge it a certain fee if you don't show up or cancel within the stated cancellation deadline.
Most reservations do not require any payment or guarantee at booking and payment is made at the restaurant following the meal.