Virtual Private Servers
For most of my sites, I stick to using shared hosting accounts, since they are very affordable and provide me with everything I need to run a normal site. I've also rented low cost dedicated servers from a handful of providers for my traffic / database intensive websites, but they give me far more resources than I could ever use (even with several websites on the same server). You really only need a dedicated server if you plan on hosting a whole bunch of websites (hundreds of even a couple thousand) or resource hog programs that I certainly don't need or use.
I recently tried a VPS account from Spry (www.spry.com) and, so far, I think its great. Virtual Private Servers (VPS) accounts are the perfect mid-level hosting solution, giving you the same power, stability and control you want from a dedicated box, but at a much lower price ($30 to $40 per month is a good price). Full root access, several sites up on the one account, multiple IP addresses, and plenty of room to grow. We'll see how good Spry is over the long run. Of course, this account uses Cpanel/WHM, my favorite, :)