Alien Invasion AU: In which the story deals with an alien invasion when canonically it does not ever happened.
All Human AU: In which characters who are canonically non-human are now humans, with corresponding changes to their backstories.
Alpha/Beta/Omega AU: Often referred to as A/B/O or even Omegaverse. It is a growing trope of AU's originated in kink memes in which characters can be Alphas (dominant males or females), Betas (ordinary working class), or Omegas (submissive males or females).
Android AU: In which the main character or most of the cast are turn into androids that serve different purposes, such as bodyguard, solider, caregiver and so on. In other cases it becomes something similar to Absolute Boyfriend, where they are mail order androids that can be order online or from a cataloged. If not, they may have originally been human but turn into an android for whatever reason.
Angel/Demon AU: When angels and demons exist (in the case of canons that don't have them) or a character is recast as one of them. However, these kind of AU's don't necessarily have to have both beings in the story as some tend to focus on only one of them.
Arranged Marriage AU: Similar to the Marriage Law AU, only the difference is that not all the characters are required to be married. It is mostly focused on only one pairing and it is usually a pairing that wouldn't normally get together such as crack ships or doomed ships. In some stories it is a plausible idea, but in others it is not.
Avatar AU: Where the characters are characters from Avatar: The Last Airbender.
YOU ARE READING
The AU Dictionary
DiversosA book explaining all of the different AU's. None of these belong to me. I got this from a blog I saw.