Some of them use external CPUs, but newer generation ones such as the FPGA Arcade can hold pretty much the entire machine include the CPU in the FPGA (usual exception is RAM, and a micro controller to bootstrap).
See FPGA Arcade, Natami, Minimig, C-One, Chameleon and others. Natami is the most capable of the bunch (aiming to be a faster, better Amiga), while Chameleon is probably the smallest (the size of an old style Commodore 64 cartridge, and can plug into a real Commodore 64, since it started as a C64 expansion on steroids, but it can run standalone too), with FPGA Arcade a nice middle group (fits in Mini-ITX form factor boxes, but isn't deep enough to fill nearly all of the box).
FPGA Arcade: http://www.fpgaarcade.com/ Chameleon: http://www.vesalia.de/e_chameleon.htm