How many Mame roms are there

MAME currently boasts it's configured to emulate about 6000 roms, and many of those can have multiple rom files to make one game. These multiple files are commonly refered to as a "parent" rom and various romsets.

An example might be one game like galaga thats originally a japanese game, that rom is the "parent", and a smaller romset can be added to translate to another language.

Keep in mind that not all of these are playable yet. A more conservitive number of working roms is 2000.