Hypnophobia or somniphobia is the fear of sleep.
Hylophobia is the fear of trees, forests or wood.
Hydrophobia is the fear of water, frequently noted as a common symptom of rabies.
Homophobia is the fear of homosexuals or of homosexual relationships; homophobic.
Hippopotomonstrosesquipedaliophobia is the fear of long words.
Hexakosioihexekontahexaphobia is the fear of the number 666.
Haemophobia is the fear of blood.
Isn't it a bit unnerving that doctors call what they do "practice?"
Heliophobia is the fear of sunlight.
Haphephobia is the fear of being touched.