Yes, FPGA implementations exist for some classic systems, including some game consoles.

Here are some relevant links (I'm sure there will be other systems that have been recreated in FPGA form):

http://www.retrocollect.com/News/super-nintendo-recreated-in...

http://hackaday.com/2013/01/23/stuffing-an-nes-into-an-fpga/

http://www.sega-16.com/forum/showthread.php?12847-fpgagen-a-...

http://www.fpgaarcade.com/platforms/

https://en.wikipedia.org/wiki/1chipMSX