It is almost better to answer this question with "what can't the Anti-Monitor do?"
Okay, aside from being really big and incalculably strong, there is the standard supervillain energy bolt projection, ominous staring, and reality manipulation. The one outstanding power he has is the ability to absorb the energy of parallel dimensions for personal use while destroying them. He also has the ability to boost the powers of another individual to a ridiculous degree (like he did with the Psycho Pirate during the Crisis). He can also create anti-matter minions that can kill people with nothing more than a touch. This cost the lives of the original Dove (Don Hall), Solivar (King of Gorilla City), the original Green Arrow of Earth-two, and countless others.