Aziraphale can create and banish items at will, alter his surroundings, make people disappear and alter memories (although these last two he's very very unlikely to do). He can also heal, move from one place to another extremely quickly, and he knows if someone is lying. He can discorporate and possess other people's bodies, and can in some cases undo other possessions. He has wings, and can fly.

And he can, through the use of what seems in canon to be a summoning circle, communicate with Heaven.

Most of these, though, he doesn't do except for personal convenience, or if specifically asked.

Mostly what he does is make very good tea which is totally an inherent ability.