The system requirements will mainly depend on what you intend to use your computer for. For instance if your going to be running a full desktop environment then your going to need a more powerful pc then if you were just running the console for some simple services. Generally if your going to be running a full desktop environment with multimedia apps open and internet programs your going to need at least a Pentium 500, with 64mbs of ram. Some people would argue that you could run it on a slower processor but if you want some reasonable speed the more power you can get the better.
Ram wise I wouldn?t use anything less then 64mbs worth and its normally recommended when using a GUI that you have at least 128mbs. We had Redhat 7.2 running on a Duron 800 with 128mbs of ram and even that was slow occasionally. If your going to be running something less advanced with no GUI then you should be fine with a Pentium 166.
The other big consideration you are going to need to take into consideration is hard drive space if you want a full desktop environment and all the programs you need your going to need at least 2-3gbs of free hard drive space just for the programs. You can fit Linux onto around 300mbs of hard drive however this wont be a lot more then a console system. If you install the maximum number of packages on some distributions then you could be looking at 4-6gbs of hard drive space.
This is fine if you have a large hard drive but for people will smaller drives you will either have to watch what you install or invest in a more up to date hard drive. Linux should automatically pick up and configure most PCI cards including sound cards, graphic cards and network adapters. The only problems I had was configuring TV cards, Mandrake configured it automatically for me and it worked first time while SuSE and Redhat left me to configure it for myself. ISA cards may need some configuring however it is possible to get most hardware working in Linux.