The great majority of Basidiomycetes produce 4 spores per basidium, one on each corner like a 4-pointed crown. However, some deviate from this pattern: a notable example is Agaricus bisporus, the common mushroom you buy in shops, which as the name suggested produces 2-pronged basidia with two spores. Cutting a very thin section through a gill and squash-mounting it should allow you to see the basidia and spores under x400 magnification.
While a single meiotic division leads to the formation of 4 basidiospores, in some basidiomycetes this is followed by rounds of mitotic divisions resulting in 4 long spore chains that grow on the basidium. In such fungi the number of spores produced from a single basidium is limited only by the number of mitotic divisions. In Cryptococcus neoformans for example the total number of spores forming four chains on a single basidium can approach over a 100.
Basidia produce one set of spores, which to my knowledge can range from 1 to 8 (e.g. Corticiaceae). You sometimes find odd-numbered spores, but the spores are generally produced in pairs.
The typical number is 4, but 2 is rather frequent because of dikaryotic spore state (as in Agaricus bisporus) and more than 4 can be observed in heterobasidia (6, 8 or more, as in Tulasnellales) and in the case of yeast-like sporidia formation (basidiospores budding as in smut fungi)