I've always found that catching a taxi is very easy. There are taxi stands at all of the parks and most of the resorts have them right outside of bell services/valet. For the Deluxe resorts, I've always been able to step outside and hail one. As the PP said, all of the taxis that can pick-up guests in WDW are run by Mears (there are a couple of different companies, but they're all Mears in the end). I think you can get to most places for less than $25 plus tip.