Thrym only shows up once in the whole medieval Icelandic poetic record, but it's an important appearance: Thrymskvitha is named after him, after all. (It means "Lay [short poem] of Thrym"). Unfortunately for Thrym, he doesn't come off so well here. First, he steals Thor's hammer, then he's too stupid to realize that the six-foot-tall, brawny "woman" with crusty eyes and a stomach big enough to hold an ox is actually Thor in disguise. Big mistake, Thrym.
The story of Thrym's theft of Thor's hammer was so popular that every up-and-coming poet wanted to tackle it. It was sort of the James Bond of its day, with remakes occurring on a regular basis. In the 15th century, rímur, or poems with extremely detailed and complex rules of alliteration and meter, were all the rage in Iceland, so Thrymskvitha got the rímur treatment.
In this Swedish folk song (also known as Hammar-Hemtningen), the story from the Thymskvitha remains pretty much the same, but all the characters get new names. Thrym's new name is Trolletrams, but don't feel too bad for him: Freyja gets saddled with "Miss Frojenborg."
Any World of Warcraft fans out there? Maybe you can help us figure out what it means when gamers say Thrym is "a level 80 elite flesh titan found in Zul'Drak." In any case, it seems that Thrym is a bit of a Frankenstein's monster here—his body is created from the corpses of other giants.
He may have gotten short shrift in the live-action version of Thor, but Thrym plays a big role in this animated film from Marvel. He lays siege to Asgard to retrieve a sword that Thor's gotten his hands on, and spares Thor's life when he gets the chance to kill him. In fact, he's almost a good guy. Almost.