NOTE: Please read legal implications on MAME™ ROM usage from Northwestern University Law School before downloading any ROMs to ensure legal compliance.  We cannot provide any instructions or information on how to download MAME ROMS due to the lack of legal options to purchase the ROMs and for us to ensure we comply with publisher's copyrights.

ROM files are the arcade games that were sucked out of the real arcade machines. The MAME™ software pretends to be the real arcade machine to run these ROM games on your PC. No ROM files are included with the MAME™ software, nor do we host any of these files.

If you own the original games, (like the JAMMA PCB), you can have the ROM. Here is information on MAME.

Handling and updating of ROMs and Sets used in MAME is probably the biggest area of confusion and frustration that MAME users will run into. The Official MAME ROM Documentation section aims to clear up a lot of the most common questions and cover simple details you’ll need to know to use MAME effectively. Also, the versions of ROMs you use should match the version of MAME you are using, or they will not work. 
You can use ClrMAMEpro to audit and fix your ROMs, a guide for using it can be found here.

ROM files are in .zip format, you do not extract them.

Put zipped ROM files in the /roms subfolder in MAME. So for example, if MAME is installed in the c:\ drive, you would find the ROMs folder in c:\MAME\roms\