One additional problem is that if you find an FPGA the packages aren't typically suitable for breadboarding. Some smaller devices will have SMT packages such as TQFP that you could potentially remove and install onto a TQFP to DIP adapter, but some are just about impossible to deal with at home coming in high density BGA packages.
For reference a TQFP package is a kind of quad flat package that has surface mount pins extending out from around the outside of the package, the pitch (gap between pins) varies depending on the size but 0.5mm is a common one. With some practice and fairly basic tools they can be removed and resoldered at home. The pins are sufficiently small that they need to be soldered to a circuit board however. You can get TQFP to DIP adapters where you solder the chip on top and 0.1" pins extend down that can be plugged into a breadboard.
A BGA is a ball grid array that has balls at the bottom of the package that aren't even visible when viewed from the top, so hand-soldering them one-by-one isn't an option. Specialty equipment is needed to rework those reliably and sometimes X-ray inspection is used to inspect the solder joints because it isn't possible to see them otherwise.
The gear you're most likely to find them in such as high-end routers, switches and video processing equipment are likely to use the larger devices. Many (most?) FPGAs also require multiple power supplies and the I/O lines often aren't tolerant of higher voltages so they're also pretty easy to destroy unless you're careful with the design.
As haneefmubarak suggested Digilent make an excellent range of prototyping boards. They take care of the tricky interfacing requirements and are an ideal way to get started. I purchased one for around $100 some time ago and had it up and running with a simple design in a manner of hours.