I've never seen my South American puffer or my two red-tail, red-eye puffers puff.
Marine puffers seem to puff much more readily. As soon as you life Arothron and Sphaeroides spp. puffers out of the sea, they puff up, together with making a weird clicking noise.
I do know that male Carinotetraodon spp. puffers raise a keel along the ventral surface when displaying to females or threatening another male (Greek: "carina" = keel, hence the name). I'm not sure if this modification has changed their ability to puff generally.
Cheers,
Neale