Berserker physique and mentality is considered a super power and it actually existed. Still does in many. It gives immense strength and speed and the berserker becomes nigh invulnerable to any melee weapon damage. Sometimes can be achieved under the influence of certain drugs like PCP, cocaine, etc.
We can see in Ultra Violet part of the electromagnetic spectrum, once the lenses are removed from our eyes. It wouldn't be true UV, but quite close.
Super-speed is possible, humans can be capable of running well over 50mph. Almost double the current fastest man alive.
http://www.livescience.com/8039-humans-run-40-mph-theory.htmlMany people have similar to what can be labeled as echolocation. Especially blind people. Even seeing individuals can gain that ability overtime.
Many have precognition too. It's not psychic, it's just perfect calculations which allow the brain to predict certain events in their life.
Then there's the ability to withstand subzero temperatures.
Replacing heart with a machine that does it's job means you don't get tired easily. But i think that's in the science fiction category for now.
There are a few more superpowers in real life that are not only possible, but exist.