Obviously I like dessert wine, so it should shock no one that in my cellar, I have dessert wines from MANY countries. As I am not home to list them all, I can do some of them by memory. However, I will list some dessert wine types from the countries that come to mind, most of which I have at least a bottle or two of in my humble collection:
Australia: Muscats from Rutherglen, tawny ports, Para port, Late Harvest Semillon, Shiraz and Riesling, Tokay and Verdelho.
Italy: Vin Santo, Recioto style of Amarone, Moscato d'Asti, Picolit, LH Orvietto, Brachetto,
France: Sauternes/Barsac, Loire's LH beauties that Fred mentioned, Banyuls (great with chocolate and the best come from Dr. Parce, imo), Vin Doux Naturelles ... Rivesaltes and Muscadet etc., Alsatian Gewurztraminer, Pinot Blanc -- but more so Riesling from Vendages Tardives (LH) to SGN levels, Maury.
Austria: Trockenbeerenauslese Riesling, Welschriesling and Chardonnay; Gruner
Spain: Malaga, Cream Sherry and Oloroso/Manzanilla/Amontillado/(PX)Pedro Ximenez Sherry
Germany: Beerenauslese, Trockenbeerenauslese, Eiswein Riesling
So. Africa: Late Harvest Chenin Blanc and Sauvignon Blanc, vintage and tawny port, Vin de Constance, LH Muscadel
Russia: Massandra port and muscat
Uruguay: Late Harvest Tannat
Portugal: Various Port and Madeira styles, Setubal's Moscatels, Aged Aguardentes (isn't Brandy really wine?

)
USA: LH Zinfandel, Riesling, Muller Thurgau, Gewurztraminer, Niagra, Concord, Vidal Blanc, Viognier, Muscat Alexandria, Chenin Blanc, Sauvignon Blanc, Marechel Foch, Semillon, Norton etc. Additionally there are many styles and grapes used for port as obscure as Petite Sirah, madeira, ice wine, botrytised wines. And some lesser knowns like Muscadelle, Muscadine, Framboise,
Hungary: Tokaji (Tokay)
Canada: Ice Wine from Riesling, Vidal and Cabernet Franc
Israel: LH Concord
Greece/Cyprus: Samos, Commandaria
I am sure I will think of some more while at dinner tonight ... but this should at least provide a few more to add to the list