Those that create web sites like myself mostly rely on shared hosting, but we all dream of getting big enough to have our own server.
I moved up last sumer to a Virtual Private Server (VPS) which is like dedicated server lite. You have pretty much total control but you still share some resources.
Dedicated Servers are like owning you own private server. I have been looking at The Planet and dreaming. They have been talked well of lately at the forums I frequent. $69 per month while fair is still a little rich for me.