http://byuu.org/preservation/list-usa
The list is outdated, I have all of the USA games now.
There are 717 officially released games in the USA. I also have two that were only released in Mexico: Super Copa and Chavez II.
The official Nintendo list is actually wrong in many areas. For instance, it does list Chavez II that was never released in the states, but it does not list Chavez I that was in fact released here. It also does not list Frogger. And it has a few titles that were never released anywhere.
Anyway, best number I have for North American cartridges is 719. I do not count the Donkey Kong or Starfox competition cartridges, because they weren't for sale. Super Noah's Ark 3D and the military Super Scope games were unlicensed, so they do not count. Super Game Boy, Game Genie and X-Band Modem have ROMs but were not technically games themselves, so they don't count on my list. Right now I don't count the Exertainment two-in-one game, because it wasn't sold alone, but it probably should be counted.
I do not count multiple revisions of the same game.
You have my guesses for Japan and Europe, but those numbers are definitely wrong. Japan has lots of special-case games like ones that were only available digitally via flash cartridges (Nintendo Power cartridges), the BS-X games that masquerade as real games, the BS-X ones that are clearly only available over satellite, the BS-X data packs for various games - Same Game's may be sold in stores, some are obviously only from the BS-X Satellaview service, the Sufami Turbo data packs ...
And then there's Europe, shit. Who knows what is up with that. Which games were released in which regions, which ones were identical in multiple regions and which weren't, and on and on.
The whole thing is a giant mess :P