From what I can tell, there are 8775 different NES games in existence, totalling about 900 Megabytes.  Basically, you could fit all of those cartridges into a 1 Gb SD card  This number includes a number of the same games that were anywhere from slightly altered to be released into a different market, to those that were completely translated and those that were "hacked" to become something entirely different.  The latter is a practise first popular in China.  It's really impossible to count how many original titles there are before they were hacked or translated, but here's an idea of the numbers for different markets:
 
+1181 NES games were released in Japan
+855 in the States
 
If we assume that all the original titles were first Japanese, then we have 1181 original titles.  I do not know Japanese, so it's impossible for me to count how many games were USA exclusives that didn't make it back to Japan.  Anyway, from these I'll post how many games made it to other markets and countries as different versions specifically altered for those markets:
 
+Asia in general - 37
+Australia - 3  
+Canada - 1 (Québec, French-Canadian version of Kirby's Adventures if anyone is wondering)
+Europe in general - 192
+Italy - 1 (TMNT I)
+Sweden - 3 (Deja Vu, Shadowgate, Maniac Mansion)
+Germany - 1 (Banana Prince (WTF?))
+France - 3 (Go Shadowgate!)
+Country or market unknown - 148
+Hacks including a tonne of fan-made SMB1 hacks and those "pirated" Chinese versions - 1072
+PlayChoice-10 titles (I wonder how many of you know what that is) - 51
+Demo Versions - 117
+Directly pirated and sold to various worldwide markets - 366
+Translated by fans into various languages - 367
+Made but ultimately unlicensed - 22
+So-called "Worldwide" versions - 37
+"Overdump" versions - 1787 (Basically, what this means is that any game can have multiple ROM versions that contain extra lines of code that the NES system ignores.  The game is essentially the same.  There are not necessarily 1787 different games with an overdump version as each game can have multiple overdump versions.)
+Versions of games that were impossible to dump for one reason or another - 2229
+Versions of games that are unclassifiable - 244 (possibly versions that had to be updated because of programming or manufacturing error)
+NES games turned into 1-on-1 player games for the arcades - 57

Oh the fond memories

I was wondering why they'd release Teenage Mutant Ninja Turtles specifically for the Italian audience, out of all the other games.  But then I realised that it was probably because they all have the names of the most famous Italian artists.  I wonder if TMNT was big in Italy??

Oh and yes, I literally have nothing else to do today.  I get a day off at the hospital and I have no idea what to do with myself.  LAME.

Made but ultimately unlicensed - 22  
 
Which games are those?  

Let's see, we've got some weird stuff here that I've never heard of:
 
110-in-1
24-in-1
34-in-1
350-in-1
54-in-1
6-in-1
76-in-1
Maxi 15
 
Any of these sound familiar?  Haha.
 
I would love to try 350-in-1.  Going to see about that right now.

Huh?  Are those like 76-in-1 different games?  Are the actual Nintendo licensed games, or just cheap crappy games?

Ahh the memories. Then again, i was more a Mega Drive fan. Or the Genesis as you yanks call it!

This is it here:
 
http://www.romnation.net/srv/scree [...] -Menu.html
 
So yes, all cheap crap games

quantumsheep, the MegaDrive/Genesis is an entirely different thread!  We can start it if you like?
 
I was one of the last kids to get an NES, but one of the first to get the MD/Genesis.  I can't remember all the games I had, I think I rented many of those that I played.