Depends on the game and the tournament rules. At Evo for example, DLC characters were banned for Mortal Kombat, but not for Blazblue or Marvel vs. Capcom 3.
Of course, much of the practice comes from playing with friends. It's not uncommon to throw down at a buddies house only to discover that the DLC character you may have been playing isn't available on their system. For me, at least, that would kill any interest I would have in using a DLC character.