The Nintendo Seal of Quality is a mark found on Nintendo-made or approved equipment and games. It can be found on the packaging of consoles, games and equipment (controllers, cables, memory cards, etc), and other licensed merchandise.
The seal was originated by Nintendo of America - and was not used in Japan, only in USA and Europe. It was obvious that this was mostly a Clever Marketing Gimmick: "Look, Atari got tons of crap games, but with NES, you can't lose because we won't let bad games even get published."
The seal is a round or oval burst pattern, with text and Nintendo logo inside. It is gold-on-white or black-on-white in color. The text says either "Official Nintendo Seal of Quality", "Official Nintendo Licensed Product" or "Official Nintendo Seal".
In every single one of the Game Boy, GBC, Game Boy Advance and GameCube games I have at hand (and on every single NES, SNES and N64 game in my sister's care), the seal actually says "Original Nintendo Seal of Quality" on the packaging. The couple of US GB games I have it says "Official" etc. Thus, I think this may be an European (or at least Nordic) phenomenon.
Apparently, in 2003, Nintendo is using "Official Nintendo Seal" for everything, at least in US. It is short and sweet and not particularly difficult to parse, so that's good. (I have seen old-style seals around, though.)
The dropping of "...of Quality" may be a good move. Historically, the Seal was obviously not in any way any assurance that the game or product was of any high quality, except perhaps physically. Many, many, many excellent, but also quite a few rather bad games have been released for Nintendo platforms. After the avid gamers had sampled Nintendo's offerings, it became obvious that largest factor to getting the Seal was that the developer paid their licensing fees to Nintendo. (Personally, I found it hilarious when I saw the Seal on a GameBoy Color version of E.T. ... well, at least they didn't market it widely as a killer hit game.) Of course, the fact that you needed to pay a hefty sum to get the Seal in first place was probably enough to not let the most stupid of the stupid ideas to ever see the light of the day...
However, Nintendo did actually partake in some quality control. At very least, the physical quality was somewhere above acceptable limit, mostly due to the fact that Nintendo manufactured the games on behalf of the licensees. If you plugged the thing in, it very rarely did blow up. Also, knowing that licensees got all development information they needed, the solutions probably were a bit less hacky. Gray developers had to come up with some ingenious stuff. Legit ones made Nintendo to produce them boring gray cartridges that "just worked".
But Nintendo did actually participate in monitoring of the "quality" of the games themselves. It just happened that it didn't matter to them if the game was any good or bad, as long as the kids could play them. In other words, licenses were subject to censorship. Many titles were mutilated pretty badly - everyone who has seen Maniac Mansion on C64 and then played the NES version probably found the experience pretty tame, with sex-themed jokes removed and even the (ewww, naked lady!) statue removed. Instead of seeing a grisly, bloody murder in the beginning of Ultima VII, we hear the guy has been "kidnapped" in the SNES version. And all explicit Nazi references in Wolfenstein 3D SNES version had to go, they even took away Hitler's moustache...
Maybe the dropping of "...of Quality" was also an indication of a little bit more relaxedness on this matter. Many a moon ago, Nintendo had to back down on the censorship in the N64 era when the competition started to make rougher games. In recent years - especially with GameCube and GBA - Nintendo has also actively tried to shake off the label of "Nintendo is for kids only" and there's a wide selection of games targeted for more mature audience.
(Apparently Nintendo of America still censors some things, but that's considerably less censorship than they used to do...)
Nintendo is not happy with unlicensed game development and employs a number of measures to hinder such thing. However, apart of consoles themselves, there has been quite a lot of hardware that is not Nintendo-approved and is still openly marketed - and, quite obviously, there's not much Nintendo can do about it, except to issue their official stance:
"Nintendo recommends against the use of any unlicensed game or accessories. Unlicensed products and accessories do not undergo Nintendo's testing and evaluation process. They may not work at all with our game systems, they may have compatibility problems with certain games or accessories, and they could possibly damage the system."
(And sometimes, I do sympathize. Got to get me a Sealed GBA light, if there even is such thing, this Chinese crap won't work and it eats batteries like popcorn. And I don't mean a literally sealed light, silly. And I just cartridge-blew an un-Sealed GCN memory card. Cartridge blowing shall never die!!!1!1!)
There is certain number of fear, uncertainty and doubt seeds in the statement, of course. But as said, legit products were boring, they "just worked". The guy who said "buggy programs are far more fascinating than working programs" was right - thanks to unofficial products, we have obscure cartridge-blowing and supergluing rituals.
Anon. Licensed and Unlicensed Products. Nintendo customer support. <URL:http://www.nintendo.com/consumer/licensed.jsp>. Accessed 2003-12-13.
GameSpy Staff. 25 Smartest Moments in Gaming, #11: Nintendo Puts a Seal on Gaming. GameSpy.com, 23 July 2003. <URL:http://www.gamespy.com/articles/july03/25smartest/index16.shtml>. Accessed 2003-12-13.
Douglas Crockford. The Untold Story of Maniac Mansion. Wired Magazine, September 1993.