In theory the fastest possible speed you can go is something approaching the speed of light (very fast!) but you would need a very very powerful rocket as the faster you go the heavier you get! This is of course impossible with our current technologyโฆ
In reality humans travel much slower than the speed of light. Tim Peake at the moment on the International Space Station (ISS) is travelling at 17,500 mph and he has been doing that for 6 months.
The fastest humans have ever travelled is 25,000 mph and this was in the Apollo missions when astronauts were returning back from Earth. In the future when we start to travel to Mars we are likely to go even faster!
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