Brazil, but only if we are talking MMA.
Interesting how "Europe" was thrown on there. Maybe the "Eastern bloc" should have been thrown in there too? Fedor, Arlovksi, Cro Cop, Aleksander, Kharitonov...the eastern bloc work ethic breeds really strong fighters. Once they start getting more fighters into MMA they could well overtake Brazil, and South America as a whole. The Eastern bloc nations have a lot of men with very powerful physiques, combine that and their "You can always work harder" mindset with western training technology and you've got some mean, mean fighters.
Brazil takes it at the moment though, since they have the Vale Tudo culture, they have a lot of fighters in MMA, so we see a lot of good ones, which does help create the illusion of Brazillians being super talented, which isnt quite true, but they are good.
In terms of striking (pure striking, not MMA striking) I give it to Thailand and Europe. The Thai's have the hardest training, they train upwards of 6 hours a day, in the blistering Asian heat, some even train in the jungle! Their training is spartan but incredibly effective. Go to a Thai boxing gym (and not one of the big ones with loads of money) and they have got a few banged up heavybags, a blood stained ring and some Thai pads. What they dont have in technology, they make up for in hundreds of years of knowledge of their art and pure, unrivalled passion for their national heratige in Muay Thai. However, the Asian's naturally smaller stature means the heavier weight divisions are dominated by westerners, simply because there arent many Thai's fighting above 170lbs at all.
Above 170lbs or so, I give it to the Dutch. They have won 11 of the 14 K-1 GPs that have been held so far, and it looks like they are about to go 12 out of 15 this year. They have an amazing passion for striking sports (but not grappling, hence why there are no dutch MMA fighters, they just dont really like MMA or grappling, its all about the striking for them). They also have the large build of Europeans, they are tall and slender, not like the bulkier American physique, and makes them natural strikers, but they would be awful wrestlers (if they even tried it...). This allows them to dominate the higher weight divisions in Muay Thai and K-1.
I'm very fortunate to live in England, and in a port city nontheless, for about £25 ($48) I can get a ferry ticket to Holland, and sail there overnight to train in Amsterdam or Rotterdam, and they have some of the best gyms there. I think next Easter I might well sail over and have a couple of days there.
But as far as MMA goes, its gotta go to the Brazillians at the moment. Watch out for the Eatern Bloc though