After the video game crash of 1983-84, there were far fewer companies making video games than at the height of the second generation of home video game consoles. What companies remained focused solely on home computer games. When the NES kick started the third generation of console games and revived the console industry, few people overlooked the fact that Nintendo was a Japanese company. Nintendo thoroughly dominated the 3rd generation of home video game consoles. Sega was also a Japanese company, although its console had less impact in the United States and Canada, it still competed with Atari for 2nd place.
If you looked through the credits of most NES games (that had credits), the names would typically be Japanese names. Of all the great, classic NES games, virtually all came from Japanese developers. Some of the best known are Shigeru Miyamoto, who created Super Mario Bros. and The Legend of Zelda, Kenji Inafune of Mega Man fame, Hironobu Sakaguchi, original designer of the final Final Fantasy series, Yoshio Sakamoto, designer of Metroid and Kid Icarus, Genyo Takeda for (Mike Tyson's) Punch-Out!! and the Startropics games, and of course no list can be complete without Yuji Hori of Dragon Quest/Warrior renown.
I do not wish to be ignorant by implying that America did not have an important role to play in the third generation, as it most certainly did. Americans bought millions of systems and games and millions were spent to get them to buy those games. Success in America transformed the console from a single-country (Japan) success into a global phenomenon, even if it was not as dominant in Europe. Nor do I ignore the important contributions of several Americans like Howard Phillips, Howard Lincoln, Henk Rogers and (indirectly) John Kirby. Without them, Nintendo of America may never have been able to make the console a success.
However, when it comes to classic console games of the third generation, virtually none can be traced back to American developers. What few nuggets did come from the States were ports of well-regarded home computer games. AD&D Pool of Radiance, Hillsfar & Bard's Tale, Boulder Dash, Raid on Bungeling Bay, King's Quest V, Lemmings, Maniac Mansion, Might and Magic, Pipe Dream, Pirates!, Prince of Persia, Skate or Die!, Ultima III and IV, Wizardry I & II. Many of these games were good ports but most lost something in translation, or their appeal was lost on NES gamers.
The U.K. developer Rare cannot be overlooked in this article. Rare(ware) made great original games like Snake, Rattle & Roll, Battletoads and its sequel Battletoads & Double Dragon, the Ultimate Teamup. It also made the R. C. Pro-Am and Wizards and Warriors series. Although the latter series is uneven, #3 is quite good. Their pinball ports, Pinbot and High Speed, are probably the best pinball games on the NES.
While there were several American unlicensed companies that released NES games like Tengen, American Video Entertainment and Color Dreams, Tengen's best titles were ports of games already released for the Famicom (Alien Syndrome, Fantasy Zone, Rolling Thunder, Shinobi) by other companies and the other two were bottom feeders that almost never released good games. Many of AVE and Color Dreams games were games developed in Taiwan. Codemasters was a U.K. company that made at least one great game, Micro Machines, good ports of the Dizzy games (which originated on the U.K. home computers) and demonstrated that they could compete with Nintendo's official licensees. Camerica distributed Codemasters games in the US and Canada. There were a few decent games from the unlicensed US NES developers, but if you are looking for classics, look elsewhere/.
Most American designers were commissioned by outfits like LJN and Acclaim to make licensed games. Virtually all suck. If I had to list all the crappy licensed games made for the NES, we would be here for a while. Some of the Star Trek and Star Wars games are okay, but nothing spectacular. Games based on gameshows like Wheel of Fortune and Jeopardy fulfilled a need, but the individual games are largely forgettable.
Things are not completely hopeless on the U.S front. One arguable classic from U.S. shores is David Crane's A Boy and his Blob. I consider this as close to an official David Crane's Pitfall 3 as he ever got. The graphics were drab, the music repetitive, the controls somewhat loose and the scrolling notable for its absence. However, the design is first rate, with all the things the blob can do and all the ways you need to do it to solve puzzles and explore the game world.
Regarding the NES's two closest competitors, there were few American original games released for the SMS, and the ports were typically done by Japanese or Europeans and released only in Europe or Brazil. The 7800 had some great arcade ports, but it had a small library and few original games for the console. No classics here.
This situation would continue into the 16-bit generation. The big two consoles, the Genesis and the SNES, still had the bulk of their classics from Japan and Europe. At least U.S. game developers were starting to take consoles seriously, but it would take at least another generation or two before the U.S. could boast of parity with the Japanese and European developers. In the fourth generation, we have such lustrous titles and series like Earthworm Jim, Zombies Ate My Neighbors, Super Star Wars, the Lost Vikings, all developed primarily by US developers. LucasArts never shined on the NES, but on the SNES, it was a different story with the above and games like Metal Warriors. The Sega Genesis may be a bit more egalitarian than the SNES, but only because Nintendo really just kept hitting the home runs on its 16-bit wonder. Of course, I could mention all the sports games like Madden and NBA Jam and quality arcade ports of the Mortal Kombat series.