Can you go to the top of the Gateway Arch?

Yes you can! I've been up and it is very cool! There is also a museum, movie place, and two stores right below it.

Improvement to first answer:

Yes you can, and I think that you go up in some sort of elevator thing. When I went, It was closed since it was on New Year's day, so I'm not positive. Either way if it is closed or not, It is fun to go and see!