| A bomber is an aircraft designed to drop bombs. Nowadays, most combat aircraft have at least some capacity to drop bombs, so the definition of bomber has been changed to encompass aircraft that can drop lots of bombs, especially nuclear weapons.
While several countries have bombers today, all of the world's bombers come from one of three sources: the United States of America, Russia, and the United Kingdom. Here's a rough equivalency chart of the three countries' respective products:
USA Russia/USSR UK
B-36 Peacemaker Tu-95 Bear
Il-28 Beagle Vickers Valiant
B-47 Stratojet Tu-16 Badger Avro Vulcan
B-52 Stratofortress M-4 Bison Handley-Page Victor
B-58 Hustler Tu-22 Backfire
B-1 Lancer Tu-160 Blackjack
B-2 Spirit (THERE IS NO SUBSTITUTE)
For the most part, Commonwealth Anglosphere countries (Australia, etc.) use British bombers, and everybody else (China, India, etc.) uses Russian bombers. The United States has been less willing to export its bomber designs to allies overseas.
That said, these bombers are starting to become a thing of the past. The current vogue is smaller fighter-bomber aircraft, which have a much easier time defending themselves against attackers. Since strategic bombing isn't that popular any more, the precision attacks carried out by smaller strike aircraft are much more valuable to air force tacticians, and several military powers (France, Germany, and Israel come to mind) use them exclusively. Even the United States is having trouble deciding whether to make the next generation B-3 bomber a big guy or a little guy. | 
