If they are heavily dependant on using rain, Pokemon like Cresselia and Thundurus can be real problems for them, due to their ability to easily throw around Thunder Waves to stop Swift Swim. Cresselia can also perform Trick Room, removing the speed advantage of Swift Swim.
Manual Weather changers, in the form of Cresselia (once again), Sableye, and Whimsicott that use Sunny Day can also throw a wrench in things.
Otherwise, the aforementioned Pokemon in the posts before me are all pretty effective at dealing with the rain, though many of them are quite heavily Bug weak.
Oh right, Togekiss and Amoonguss are two other Pokemon can give rain teams some issues.
Just another rainy day on the train...
VGCS Jaunary International, 165W-30L-27D/C, 1873
, 13th Place
VGC 2013 Winter Regional, Salem OR, 1st Place