I don't usually do copy and paste, but all the info is right here from Wikipedia. You can search for recipes for the various kinds by entering the pastry's name in Google.
Use care when making any kinds of donuts, especially around kids, as many involve very hot oil. One thing we used to do when I was a kid, though, was to make quick and yummy donuts using the Pillsbury pop'n fresh style biscuits. You just punch a hole in the center and cook them in hot oil, and when they are done and cool you roll them in cinnamon sugar or powdered sugar or whatever. It's not international, but if donuts is your theme it's an easy, no mix way to make some!
Caution--Hot Oil!!
Argentina
In Argentina, the local equivalent to doughnuts are facturas, a popular baked doughnut-like pastry of German origin. Facturas are consumed massively and can be found in every corner bakery. However, doughnuts are starting to gain popularity, probably because of American influence through television series and films. They can be found in some bakeries and hypermarkets like the American Wal-Mart or Chilean Jumbo.
Australia
In Australia, not only do they have the traditional doughnuts, they're also famous for their own jam doughnuts. These doughnuts are sweet buns that have a filling inside. Other fillings inside these doughnuts include custard.
Austria
In Austria there is no real market for American-style donuts. Not a single nationwide donut chain exists; the only store making itself quite famous selling donuts is the Viennese store Batriks Donuts.
The Austrian doughnut equivalents are called Krapfen. They are especially popular during Carneval season (Fasching) and do not have the typical ring shape but instead are solid and usually filled with apricot jam (traditional) or vanilla cream (Vanillekrapfen).
Belgium
In Belgium, the smoutebollen are similar to the Dutch kind of oliebollen, but they usually do not contain any fruit, except for apple chunks sometimes. They are typical carnival and fair snacks and are eaten with powder sugar on them.
Canada
In Canada, the doughnut follows the same design as in the United States. Several stores including Tim Hortons, as well as some U.S. chains such as Dunkin' Donuts and Krispy Kreme, make the majority of their profits by selling donuts. Another Canadian variant is the Beaver tail (known as an "elephant ear" in many other countries).
Per capita, Canadians consume the most doughnuts in the world, and Canada also has the most doughnut stores per capita.[5] Many humorous Canadian stereotypes, such as the Bob and Doug McKenzie characters, include doughnuts (as well as stubby beer bottles, tuque hats, maple syrup, and back bacon) as part of their lore.
China
Chinese cuisine features long fried doughnut sticks that are often quite oily, hence their name: Youtiao (Mandarin, lit. oil sticks); these pastries are not sweet. In Cantonese, this doughnut-style pastry is called yow ja guei. Often this is served with the traditional rice porridge of Chinese cooking, congee. A type of sweet Chinese doughnut is the oval shaped fried pastry called "gnou lay sou", which translates to "Ox-tongue pastry" due to its tongue-like shape. Chinese restaurants in the US sometimes serve small fried pastries similar to doughnut holes.
Croatia and Serbia
Doughnuts similar to the Berliner are also prepared in the Northern Balkans, particularly in Croatia (pokladnice or krafne) and Serbia's Vojvodina province. They are called krofna or krafna,[citation needed] a name derived from a German word for this pastry. This type of doughnut is popular in Chile because of the large German community there and is called a Berlin (plural Berlines). It may be filled with jam or with manjar, the Chilean version of dulce de leche.
Denmark
In Denmark, doughnuts do also exist in their "American" shape, and these can be obtained from various stores, e.g. McDonald's and most gas stations. The Berliner, however, is also broadly available in bakeries across the country.
France
In France and in New Orleans, Louisiana, there exists a fried pastry called a beignet, which is sometimes described as a French doughnut.
Germany
In Germany, the doughnut equivalents are called Berliner (sg. and pl.), except in the city of Berlin and some other German areas, where they are called Pfannkuchen. In middle Germany, they are called Kreppel. In southern Germany, they are also called Krapfen and are especially popular during Carneval season (Karneval/Fasching) in southern and middle Germany and on New Year's Eve in northern Germany. Berliner do not have the typical ring shape but instead are solid and usually filled with jam. Bismarcks and Berlin doughnuts are also found in the U.S., Canada, Finland, and Denmark.
Greece
In Greece, there is a doughnut-like snack, called loukoumas (λουκουμάς), which comes in two types (one is shaped like the number 8; the other is torus shaped like the number 0), from which the first one is crispier, whereas the second one is larger and softer.
Iceland
In Iceland kleinuhringur (pl. kleinuhringir and kleinuhringar) are a type of old Icelandic cuisine which resembles doughnuts.
India
Some savory, fried items not based on wheat-flour pastry are referred to as doughnuts, such as the ring-shaped Indian vadas, made of lentils. Indian vadas are food of masses. In north India, vadas are soaked in curd, sprinkled with spices, topped with sweet/sour chutney and then eaten. In south India vadas are eaten with sambar. Also, there is a doughnut like sweet made in India called "badushah". This is made like an old-fashioned doughnut by frying the dough in oil and then soaking it in sugar syrup, and sometimes flavored with spices.
Indonesia
Donat Kentang is known as an Indonesian style potato doughnut; a fritter that comes in ring shape and is made from combination of flour and mashed potatoes, coated in powder sugar or icing sugar.
Iran
Persians are known for their zooloobiya, a fritter that comes in various shapes and sizes and coated in a sticky-sweet syrup.
Israel
Jelly doughnuts, known as sufganiyah (סופגניה, pl. Sufganyot סופגניות) in Israel, have become a traditional Hanukkah food in the recent era, as they are cooked in oil, associated with the holiday account of the miracle of the oil. Traditional sufganyot are filled with red jelly and topped with icing sugar. However, many other varieties exist, with the more expensive being ones filled with dulce de leche.
Italy
Italian doughnuts are called ciambelle, krafen, zeppoli or bomboloni.
Japan
Mister Donut is one of the most popular doughnut chains in Japan. Native to Okinawa is a spheroid pastry similar to doughnuts called sata andagi.
Lithuania
In Lithuania, a kind of doughnut called spurgos is widely known. Sometimes spurgos are similar to Polish doughnuts, but some specific recipes, such as cottage cheese doughnuts (varškės spurgos), have also been invented.
Mexico
The Mexican donas are very similar to donuts including in the name; the dona is a fried-dough pastry-based snack, commonly covered with powdered brown sugar and cinnamon, white sugar or chocolate.
Netherlands
In the Netherlands, the Oliebollen, referred to in cookbooks as "Dutch Doughnuts", is a type of fritter containing pieces of apple and/or dried fruit like raisins; they are traditionally eaten as part of New Year celebrations.
Poland
In Poland and parts of the U.S. with a large Polish community, like Chicago and Detroit, the round, jam-filled doughnuts eaten especially—though not exclusively—during the Carnival are called pączki (pronounced [ˈpɔntʂkʲi]). Russian "пончики", ponchiki, and Ukrainian "пампушки", pampushky, are the equivalent designations for pączki, but are usually not filled with jam. Romanian gogoşi are similar to the Polish pączki. Pączki have been known in Poland at least since the Middle Ages. Jędrzej Kitowicz has described that during the reign of the August III under influence of French cooks who came to Poland at that time, pączki dough baked in Poland has been improved, so that pączki became lighter, spongier, and more resilient (see pączki in Polish Wikipedia).
South Africa
In South Africa, a variation known as the koeksuster is popular.
South Korea
Many bakeries in South Korea offer doughnuts either filled with or made entirely from the Korean traditional rice dessert tteok. These come in a variety of different colors, though they are normally in green, pink, or white. They are often filled with a sweet red bean paste or sesame seeds.
United Kingdom
In some parts of Scotland, ring doughnuts are referred to as doughrings, with the doughnut moniker being reserved exclusively for the nut-shaped variety. Glazed, twisted rope-shaped doughnuts are known as yum-yums. It is also possible to buy fudge doughnuts in certain regions of Scotland. In some parts of Northern Ireland, ring doughnuts are referred to as "gravy rings" due to their being cooked in oil, itself colloquially known as "gravy".
United States
A popular doughnut in Hawaii is the Malasada. Malasadas were brought to the Hawaiian Islands by early Portuguese settlers and are a variation on Portugal's filhós. They are small eggy balls of yeast dough deep fried and coated in sugar.
To celebrate Fat Tuesday in southeastern Pennsylvania, churches sell a potato-starch doughnut called a Fastnacht (or Fasnacht). The treats are so popular there that Fat Tuesday is often called Fastnacht Day.
The Polish doughnut, the pączki, is popular in U.S. cities with large Polish communities such as Chicago, Milwaukee, and Detroit.
