Can I run 1 wire from my router to a hub in my room to connect a computer & 2 xboxs instead of running 3 wires to my room?

I would rather use a switch to have all three systems connected to it and one wire running to the router...

Can i run 1 wire from my router to a hub in my room to connect a computer & 2 xboxs instead of running 3 wires to my room?
Yes, depending on the hub, it may have to be what is called a crossover cable. Most broadband "router/firewalls" support 254 computers connected to them, even though they may only have 1 to 4 hub ports on them.

Hub is peace of crap if you want a good full connection from what your provider gives. I would rather say switch is a good thing although they are working on the same layer on OSI but switch is dilevered the full bandwidth with-out striping or dividing. It means you can gain an access in a good way