The legendary musician Orpheus descended into Hades to rescue his wife Eurydice. He was allowed to, with the caveat that he couldn't look back until he got back to the mortal world. He failed and thus failed his quest:
So, a quest to the Underworld should probably have an unusal or arbitrary failure condition, but one known to the questers.
When Hades kidnapped Persephone to be his bride, her mother went to the Underworld to get her back. Persephone had eaten six pomegranite seeds (or was tricked into eating them, I've read different versions,) and was required to stay with Hades six months out of the year.
From this I take the idea that you shouldn't eat or drink anything while in the Underworld: bring food and water.
Hercules had to kidnap Cerberus ("Spot," no, seriously,) the hound of Hades as one of his labors. While he was there he found his friend Theseus glued to a chair, and ripped him loose, leaving Theseus' rear end "behind."
So: treasures and old friends not directly related to the quest at hand are there to be had, but they may bear a cost.
I also found this page, Myth Encyclopedia: Underworld, which has a few I'm unfamiliar with. I need to track a longer version of each down (Mulian rescuing his mother from Buddhist Hell seems really interesting.)
If you're aware of any others, feel free to post about it in the comments. I'm really looking for inspiration for this one and any help is appreciated.