Slingbox (
www.slingbox.com) has something called the Slingcatcher which lets you put stuff on your computer to your TV. It works nicely.
Also check out Tiger Direct (
www.tigerdirect.ca) or NewEgg (
www.newegg.ca) for Media Players that can do this as well. They are called Media Extenders.
You wont see your screen using these, but you will see videos.
If you provide the specifications of your computer, I can give you some advice. Years and years and tens of thousands of dollars spent on building my own personal media center heaven have taught me a lot.
At the very least you want to have the following:
HDMI or DVI out. If you have DVI, you can buy an adapter for this
A TV with multiple inputs (or a stereo) that can do 1080p (Hi Definition)
If you are looking to be able to browse the web, share Youtube and such, you might want to look at buying the PS3 which I think is the most capable, single box solution out there for playing DVDs, Blu-Ray, Video Games, acting as a Media Extender (for movies/TV/Music on your computer and network), and as a very capable web browser that you use to watch Youtube, Google Videos, iStream and JustinTV.