Daemon and Aemond (and their respective dragons) both perish at the Battle Above the God's Eye. Aemond's body will eventually be recovered (with Daemon's sword Dark Sister stuck in skull through the eye socket), but Daemon's body or bones will never be found.

There is speculation that he didn't actually die, but instead went into seclusion with Nettles and lived out a quiet life away from all of the political fighting that defined his life.

I think that all of the stuff he's seeing at Harrenhal is going to burn him out or give him the self-realization that he doesn't want to continue on this path, and we'll find out that he doesn't die at the God's Eye but instead left his sword behind and went away with Nettles (whose arc as Daemon's lover might be passed on to Alys Rivers if they don't introduce Nettles and give her arc to Rhaena) as has been speculated. If Daemon does run off with Alys, then he'll probably end up raising Aemond's child who she'll get pregnant with after he takes Harrenhal and executes the Strongs.