In the American civilian market, the AR-15 is definitely ascendant, although oddly enough, the best selling gun at Bud's for the past 2 years has been the 91/30. On an international level, the AR has not been militarily ascendant, but its cartridge has been adopted almost everywhere. In the general international community, three guns reign supreme: the AKM, the 91/30, and the FAL. The AR family isn't actually all that common or celebrated outside of North America. Other continents and countries have their own traditions and platforms. In the EU, bullpups are quite common. The British have their L85, the French have their FAMAS, the Austrians have their AUG, with other designs on the way.
In other parts of the world, the AR is much less of a big deal, though it still carries weight as the symbol of American martial might, whether that is a good thing or a bad thing. The AR is not very popular in Africa, with much of the continent being either third or fourth world countries without the same sorts of manufacturing quality or relative field cleanliness; in a continent abound with deserts, jungles, and savannah, a gun with absolute proven reliability which will work while dirty, unlubricated, and abused, is an absolute must. There is also the issue of the 5.56 not being highly effective on two things commonly found in Africa: dangerous large beasts and small malnourished men. That is why there, old style bolt actions firing full power 30 caliber ammunition are still very popular and common. The militaries of Africa prefer powerful, sturdy, reliable rifles with common, powerful ammunition. 29 countries in Africa issue the FN FAL or some licensed variant. The FAL is much heavier than the AR, it has more recoil, and it's a more old-fashioned weapon, but it is known for working every time you pull the trigger and bringing your target down in short order. African militaries also issue a lot of AK type guns. 32 African countries issue the AKM or produce it under license, and even more issue an AK variant or something spawned from the AK, either purchased from Russia, produced under license, or produced without license. For stopping power that definitely goes boom every time and has a ubiquitous supply of ammunition and parts and guns, the Kalshnikov is extremely popular.
In Europe, the AR itself is not all that influential. In most countries, it is forbidden for ownership by civilians. However, its design features show up in weapons inspired by it in one way or another. All NATO assault rifles are chambered in its 5.56x45 round. It was the first popular, accepted polymer gun in a small caliber. Its adoption brought about a reduction in calibers, changes in military tactical philosophy, the creation and adoption of more polymer guns, a market shift towards making the weapon as light as possible, and the start of crating modular weapons where one lower receiver can be mated to a variety of upper receiver, which can be mated to a variety of accessories. Its controls were the beginning of a move for purpose built ergonomic controls and keeping the same layout for different platforms, as well as giving a bit of assistance towards lefties, which resulted in the modern ambidextrous weapons being introduced.
The AR is somewhat influential in Asia. Granted, its influence is somewhat markedly less than in Europe, but it is felt. The AR was favored by the Army of Vietnam, whose soldiers were shorter and lighter than those of the western nations, coming in at 5'6"-5'3"; at to just below average globally. The smaller round and light recoil made the gun easier to handle, and its shorter length and reduced weight was also handier for the shorter Asians. Along with US aid and troops, AR's poured into the area. However, the AK won the region, being as reliable and abundant as ever, and being in really cheap blunt supply from the USSR and PRC, in addition to its role in the Communist revolutions and counter revolutions in Tibet and Afghanistan. It has become the gun of choice for guerrilla and insurgent groups, and is the main weapon for factions on both sides of the law in the Middle East, as well as the weapon of Jihad and the governments opposing Jihad.