Empathetic Memory

Peter's initial power is the ability to copy the powers of those who are close to him. He later learns to recall these abilities by focusing on his feeling towards these people and has even been shown using multiple replicated powers at once.

Precognitive Dreams

Peter's first absorbed ability that we learn of is his ability to have dreams of future abilities. In the opening of the first Season Peter dreams of flying which is one of the first powers he ever receives.

Flight

Peter Petrelli has the ability to fly and can do so while carrying at least one other person.

Precognition

Peter has the ability to draw and paint the future. He was able to make many pictures of prophetic nature many detailing the destruction of New York City.

Rapid Cell Regeneration

Peter has absorbed Claire's ability of Rapid Cell Regeneration. This allows him to heal from any injury or disease. Additionally his blood can be used to heal other of nearly any injury or disease up to and including recent death. This ability cannot be used to heal cancer however as the rapid cell growth actually makes cancers worse.

Peter heals from having his skull cut into

Peter's regeneration even allowed him to survive a nuclear explosion that wiped out a city from point blank range.