Way to open a can of worms! :p I mean seriously, what are you looking for in a computer? And what's your budget? Etc...so many questions that need answering.
If you just need a basic machine and have little knowledge about computers, I say go Dell. Pretty much the best mainstream vendor. Stay away from HP and Compaq, they use too many proprietary parts and their aesthetic designs suck. If IBM still makes desktops you could try that too, I haven't kept up with IBM at all, even though I used to work for them, but I used a laptop for work, IBM's mantra is all about the laptop!
If you're fairly literate about computers and are into gaming or other high-end applications, look into the boutique vendors like Alienware, Voodoo PC, Falcon Northwest. They're expensive but perform very well and everything is upgradeable, plus they all do the trick-out features, like case modding/paint jobs, organized wiring, case cooling setups, etc.
I take it by your comment that you don't have the know-how to assemble a computer from parts bought online, which is obviously the best route.