I have the cheapest-of-the-cheap double jogging-style stroller. I can't even remember the name, but we bought it at Toys R Us 2 years ago. DD is too old for a stroller except when we go to WDW, so we figured it would be OK to go on the cheap for something we would use so infrequently. Anyway, the only place we ever had a problem was going through the MK gates.
However, we learned that a couple of the gates on the far left (as you stand facing the entrance) are wide enough to accomodate our behemoth of a stroller. Unfortunately, these gates aren't always open at closing time. So on my solo trip with DD and DS, we relied on the kindness of strangers. Two fabulous gentlemen, who were obviously great dads, lifted the stroller -- full of 65 pounds of sleeping children -- over the gate for me during the closing time rush.
Other than that, no problems at all. Bear in mind that all of WDW is handicapped-accessible, above and beyond most accesible places, and most double strollers have dimensions that are similar to the larger wheelchairs. I think my stroller is an exception to this, but even so, we only encountered one obstacle.