Wikipedia has some revealing information here:
Not all puffers are necessarily poisonous; Takifugu oblongus, for example, is a fugu puffer that is not poisonous, and toxin level varies wildly even in fish that are. A puffer's neurotoxin is not necessarily as toxic to other animals as it is to humans, and puffers are eaten routinely by some species of fish, such as lizardfish and tiger sharks. Also, Japanese fish farmers have grown nonpoisonous puffers by controlling their diet.
It seems that susceptibility to tetrodotoxin varies a lot from one animal to another, and so some natural variation might allow a reasonable amount of predation to occur. I also wonder whether the variation in the amount of toxin in the fish implies that the fish are often depleted.
There are cases of animals who have evolved a resistance to Tetrodotoxin, but for the most part its may the predators you are thinking of. The toxin is synthesized by a symbiotic bacteria and is found not only in fugu but also blue-ringed octopus, rough-skinned newts and some sea slugs. These animals probably all began with enough intrinsically low sensitivity to the toxin to take on the symbiont and probably evolved to be completely insensitive. To find a predator that would have co-evolved a similar resistance you would look for a predator that particularly favors the envenomed animal. In the case of the rough skinned newt, its suspected that the common garter snake is an example of such co-evolution. Others may be out there to discover - its probably difficult to watch marine animals to know what their typical predators are.