In my opinion, the best nation in the entire world right now for producing boxing talent is Ukraine. In the 2011 World Amateur Boxing Championships they led the entire world with 5 medals, 4 of which were gold. In the 2012 Olympics, they tied with the UK for the most medals in the world, with 5 (keep in mind that UK was clearly favoured in that the Olympics were held in UK). In the amateur ranks, Ukraine has Vasyl Lomachenko, who is arguably the best amateur boxer of all time. In the professional ranks, Ukraine has Wladimir and Vitali Klitschko, heavyweight rulers. Ukraine really is the global powerhouse when it comes to boxing and their numbers in the past 3 or 4 years demonstrate that.
One of the reasons why Ukraine is so good is because they have a top notch amateur system and the sport is popular among the youth. The sport is popular there and no doubt that is largely due to the Klitschko Brothers' successes. The K Brothers have invested in boxing in Ukraine (opening gyms and giving money to sports charity in Ukraine), and cards are usually held in Ukraine atleast several times per month. Their amateur formula is highly successful and thats why they have some great pro's as well. From an economic standpoint, the relatively lower cost of living and earning in Ukraine may contribute to their boxing success.
Other nations that produce particularly world class boxing talent include UK/Ireland, Russia, and Cuba (mostly blacks). Ireland as a nation only has a population of 3 million or so, but is responsible for producing some absolute top level world talent, capturing 4 medals at the last Olympics compared to USA which has a population of 300+ million but failed to capture a single medal. Lastly, some countries which aren't quite world class but still produce solid boxing talent include: Japan, Romania, Germany, Bosnia-Herzegovina, South Africa, Argentina, Slovenia, Serbia, Mexico, USA, Brazil, Poland, Azerbaijan, Philippines, China, India, Kazakhstan, Uzbekistan, and Colombia. Kazakhstan is an interesting case, and say 8 years ago was a leader in the sport. They had a guy, I still remember his name Sarik Sapiyev I think it was, I saw him at the Olympics he won gold and I was ***so impressed*** with him. He never went pro, a pity. Of course they also produced Golovkin who is killing it today in the pro ranks!
Here where I live in Canada, our boxing scene is mainly centered in Montreal and I have to admit, it is quite good! Montreal has had some amazing pro fighters in recent years and that is because boxing has always been popular in Montreal. Additionally, Montreal has a great youth system and that shows later on when the fighters go pro. Arturo Gatti, Jean Pascal, Lucian Bute, Leonard Dorin, Dave Hilton are all recent world champions out of Montreal!
One of the most obvious shifts in recent years in the sport of boxing has been Americans losing ground to Europeans. Another shift that is starting to take place *now*, I would say, is that China and India are starting to field more competitive teams. They probably won't win anything for a while, but say 10-15 years from now, I think we'll be seeing some Indian gold medalists and pro boxers.