I'm in the computer science program at RHIT and we're required to take two courses on computer architecture. In the first course, we implement a simple processor using an FPGA, then we design and build our own. Of course, this is before we learn about pipelining, but it's still a lot of fun. In the prereq course where we learn digital circuits, my section's final project was to build a judging system for a pinewood derby race using an FPGA, and other sections had to do such things as implement an alarm clock. I had a lot of fun doing both and they really made me appreciate digital hardware.
Also, as a fun side note, a roommate of mine last year designed on paper a Brainfuck interpreter that ran off raw Brainfuck ASCII source for the Xilinx FPGA competition, but never built it because he wasn't sure if he could present on Brainfuck without laughing. I wonder if that schematic is still lying around somewhere...