I'm not sure, I don't ever remember it being an issue.
I remember a lot cartridge piracy happening, particularly for the Nintendo SNES. You could get a third-party box, which came directly from China of course, that plugged into the SNES, and the Sega Megadrive, that had a 3.5in floppy drive on it. Games were much cheaper on floppies than carts, and usually they came from markets, unscrupulous video rental stores and mail order. This was in the UK.
I only remember game piracy being an issue when the Sony Playstation was introduced, then onwards from there it was a problem. I do not remember hearing anything about cartridge games in the 90s
Cart piracy was a big problem, especially in the UK, because I knew the people who did it. From what I know about it, Playstation piracy was very easy. With just a PC and a CD burner, and the right software. The console itself needed an inexpensive mod-chip fitted to completely defeat the black CD DRM. But with a little bit of jiggery-pokery, the mod-chip wasn't always necessary.
Copy protection schemes for games go back a long way, as it was always very easy to duplicate game cassettes for the Commodore C64, Sinclair Spectrum, etc.
One of the wackiest, unusable and most inconvenient ones I remember was a thing called Lenslock.
http://en.wikipedia.org/wiki/Lenslock