The mother of fraternal twins in Vietnam recently had DNA testing done on her kids because they looked so different from each other. It turned out that, yup, the twins had different dads.
This is rare, but certainly not unheard of. It's called heteropaternal superfecundation, and it happens when a woman's eggs are fertilized by two men within a short period of time. It can only happen with fraternal twins, though, since they're the result of two separate eggs in the mother's womb being fertilized by two different sperm. Identical twins, on the other hand, are the result of one already fertilized egg splitting into two.