In Garfield in Paradise, Odie and Monkey driving the car into the volcano to appease the volcano's spirit. Even though it turned out to not be the Heroic Sacrifice it first appeared to be, it was still an extremely heroic thing to do.
In the prime-time TV special Garfield In the Rough, an escaped panther threatens the life of Jon and Odie. Garfield, who ran up a tree in fear, has a sudden Big Damn Heroes moment, dives from the tree onto the panther's back, clawing away at it. He doesn't actually defeat the panther, though he does buy park rangers some time to tranquilize it without anyone getting hurt.
In the Halloween Special, when Odie and Garfield are trying to flee from the ghost pirates, they have to swim across a lake since the old man who warned them about the pirates took their boat. Garfield immediately starts drowning, because he can't swim. Odie swims back to him, then pulls him to shore, all while being chased by the ghosts. This could also be border line Crowning Moment of Heartwarming, because he could have chosen to just save himself, but he cares too much about Garfield. To add to the heartwarming, Garfield, who was originally going to take all of Odie's trick or treat candy, states that he can keep it. Garfield gave up food, some food that he had been thinking of as his all along, as a thank you.