I have a desktop and a laptop both of which I use to create and edit movies, music, etc. I also like to play mid to high end games on them like C&C, Oblivion, DoW, etc. My problem is storage space and accessibility, I already have 650gb in externals filled up. I've heard a few suggestions from people at work and they seem to think that an application server might help. The idea is that i would be able to install the games on the server and store movies, music and work, then access it via a home network or, best-case senario, over the web.

Is this possible? If so what would you recommend for hardware? Also what kind of software would I need?

no, it would not, because you can not run directx off different pc's other than your own. The game files "have" to be on your hard drive. But if you do get it to work, let me know.