Typically, you're looking at either an Intel Xeon or AMD Opteron, but in truth, a server can be run from any processor. I've run web servers in Pentium 4 processors and SQL servers on an Intel Core2Quad.
RAM, as ColGeek states, really depends on the intended usage. Web servers don't require a lot of RAM where as Exchange Mail servers (last I checked) were extreme RAM hogs.
-Wolf sends