The hero of heroes puts in a pretty short cameo in his stint with the Argonauts. He does get to show off his mad monster-bashing skills when the Argo is attacked by the giant Earthbound Men, whom he annihilates almost single-handedly. Heracles' time as an Argonaut is cut short when his armsbearer-slash-boytoy Hylas is seduced and spirited away by some particularly savory water nymphs.
As he tends to do, Heracles completely flies off the handle when Hylas disappears, and the Argo is forced to sail on without him. It's probably a totally good thing that Heracles has to bail on the quest. With somebody as powerful as this son of Zeus around, none of the other heroes would've ever been able to really show off their stuff. For tons more on Heracles click here.