Desktops at home: SUSE Linux
Server: Redhat Linux
School: Ubuntu/Xubuntu
Laptop (if I'm booting from a CD): Kunbuntu PPC
I'd be reluctant to run Fedora Core on a big time production server;
CentOS is much better suited to that (it's Redhat Enterprise Linux with the Redhat branding removed distributed for free).
Anyway, one thing that I think I should mention (as you said you've been having problems with drivers) is, if your goal is to try out different distributions and learn some of the ins and outs, figure out what you like, etc. you should try out some of the
free VMware stuff; specifically the Server product has just recently left beta and I've had a lot of luck with it. If you use VMware it'll create a virtual computer on your machine and then you can install a Linux distribution in that virtual machine (or find prebuilt Linux virtual machines) which you can run at the same time as your host Operating System. The really neat thing about drivers is VMware makes it appear to the guest Operating System as though certain standard hardware is being used which Linux and most other Operating Systems you can find support; VMware can make your network access go through the Virtual Machine to your actual physical hardware. So, for example, say your computer currently runs Windows XP; you can download VMware Server, install it, create a virtual machine and install any Linux distribution you want in it and from within that Linux distribution still access your network (through VMware and Windows XP). Since the virtual machine has standard hardware that will generally get rid of all driver problems, too.
Of course, Linux isn't the only Operating System you can have as a guest in VMware. It supports Linux and Windows as host Operating Systems and anything that'll run on your particular processor architecture as a guest Operating System.