Due to my job, I've acquired a healthy aversion to FPGAs. Come to think of I've acquired a lot of aversions actually...hmm.
Once, we were in progress of debugging a particularly perplexing bug in a particular device where the design almost performed as expected...almost. The design was validated successfully through simulations, everything was supposed to work correctly. After spending some days on this issue, the FPGA vendor application engineer came to see us and told us that they just discovered a specific issue in double port memory blocks when data was not guaranteed to be written successfully in some particular cases because of analog/electrical issues concerning the memory implementation. This was exactly the cause of our bug.
In any case, good luck with your endeavor, choose a well supported family of FPGA devices, optionally decide on vhdl vs verilog and constantly recall yourself to check whether the FPGA providers' tools or opencores.org site has modules or blocks that you can easily reuse.
I'm not so sure about the utility of FPGA devices for light hobby set-ups, but that should never stop the curiosity and the interest that we have to invest in our endeavors.
As a concrete application that absolutely require a FPGA device, a logic analyzer could be very useful. There are already some open source implementations, but it's the kind of design that helps learning about all kind of stuff: data acquisition & storage, interfaces, etc.
Cheers,
Dan