Yes, there are a ton of van cabs around WDW, because of the large number of family groups. Just ask a valet or bell services CM to call you one, if you're at a hotel. If you're at a park, there's a cab stand that any CM can direct you to, and you just get into the first available van, or ask a CM to call you one. They hold up to 7 passengers, and the rates are identical to the sedan cabs.
That number given earlier (407-699-9999) is the number for Yellow Cab, which is one of the Mears nameplates. You can also call the main Mears number (which likely goes to exactly the same call center): 407-422-2222. Any of the Mears cabs will do. Mears owns and runs Checker, Yellow, City, and Safety, and maybe others. But they're all painted yellow, and they are, as Alesia says, the only ones allowed to wait at WDW locations. As I understand it you can actually call another cab company to come get you at WDW, but they can't wait at the cab stands for fares.
But you really wouldn't want to call another cab company. Mears is the dominant company for a reason, their drivers all know WDW really well, and you're much less likely to have a problem with them.