Hanahaki Disease AU: In which everything is still canon, except an fictional disease known as Hanahaki exists within it. Those that catch the disease coughs up flower petals when they suffer from one-sided love. Their lungs get filled with the flowers and their respiratory system grows roots. They choke on their own blood and petals, and die. It can be cured through surgical removal, but when the infection is removed, the victim's romantic feelings for their love also disappear. Sometimes this also removes the victim's ability to ever love again. Another way to be cured of it is for the object of the victim's love returns their affections, thus making the love no longer unrequited.
Harem AU: Or Reverse Harem AU is when a story that doesn't contain any polygamous or love triangle relationships turns into one. Usually the main character has something happen to them that attracts the other characters to them, be it from a love potion, experimental perfume, spell gone wrong, and so on.
Haunted House AU: Or Haunted Castle AU, in which a character moves into a new home or castle and doesn't know that it is haunted (usually by a ghost, sometimes a demon or some other type of creature) or they are dared by their friends to spend the night in it.
High School/College AU: In which the characters are shown in high school or in college together. They are often done with characters who canonically meet later in life, altering or entirely overwriting their original backstories. Similar to this AU is the Boarding School AU.
Hogwarts AU: In which the characters from other stories are placed into the setting of Harry Potter. These can be coexistent with Harry Potter canon, or ignore it entirely. But they are often portrayed as students of Hogwarts instead of teachers that work there.
Hospital AU: In which the characters of a story are doctors, nurses and patients in a hospital (sometimes it is set in an asylum.)
Hooker AU: Where one or more of the characters is a sex worker. The more common is the Pretty Woman-type fantasy of a hooker with a heart of gold, rescued from life on the streets by a client. Sex work of all kinds is portrayed: brothels, escorts, street prostitution, "call-girls" as well as strippers and go-go boys. Most of the time one character of the pairing is the hooker and the other the client, though some stories have both characters as prostitutes (sometimes along with other canon characters, in either a brothel-type setting or living on the streets).
Hunger Games AU: In which characters from other stories are competitors in the Hunger Games.

YOU ARE READING
The AU Dictionary
RandomA book explaining all of the different AU's. None of these belong to me. I got this from a blog I saw.