Hestia - Goddess of the hearth
Hades - God of the underworld
Hephaestus - God of fire and forging
Hera - Queen of the gods and goddess of marriage
Hesperides Tree - Tree that held golden apples of immortality
Heracles (you're welcome) - Hero famous for completing 12 labors
Hydra - Nine-headed snake. If one head is cut off, 2 heads grow in its place. Has one immortal head
Hermes - Messenger god
Hebe - Goddess of youth
Harpy - A bird with the head of a woman
Helen - Queen of Sparta
Hecatonchires - 3 humans with 50 heads and 100 arms. Guards the gate to Tartarus
Hecate - Goddess of magic
Helios - God of the sun
Hypnos - God of sleep
Hyacinth - Apollo's boyfriend who got turned into a flower
Tell me if I missed anyone/anything