One is the episode where Hercules brings Alcestis back to life by wrestling with Thanatos. This is familiar from the tragedy by Euripides named for Alcestis. The other comes from the stories about the crafty Sisyphus, king of Corinth. You may know that Sisyphus was condemned to eternal punishment in the Underworld. There Sisyphus must forever roll a boulder up a hill.
Do you know what he did that was so bad? One major mistake was blabbing about one of Zeus' indiscretions. For doing so, Zeus sent the death god, Thanatos, after Sisyphus. Sisyphus tricked Thanatos and bound him. The result was that no one could die. [Visualize science fiction B-movies.] Thanatos was rescued by Ares, but not before Sisyphus had figured out another method of cheating the Underworld, this time, not the lord of death, per se, but Hades. Once Hades recovered Sisyphus, he gave him the rock.
Thanatos was the Greek personification of death. His twin brother was Hypnos (Sleep) and his mother was Nyx. Thanatos, Hypnos, and Nyx all live at the ends of the earth. Erebus may have been his father.
In Hesiod's Theogony, Thanatos is described as pitiless, making even the gods hate him, even though he cannot kill them since they are immortal. Thanatos appears in Iliad XVI to carry back the body of Sarpedon to Lycia. Thanatos can be overcome, as when Herakles, after wrestling Thanatos, brings Alcestis back from the Underworld. Pherekydes tells of Sisyphos binding Thanatos with the result that no one can die (source: Timothy Gantz).