The most common type of bread mold, and indeed one the most common fungi in the world, is Rhizopus Stolonifer, widely known as "black bread mold". It is a thread-like Mucoralean mold (sometimes known as pin mold). This type of mold is typically fast-growing and thrives on conditions associated with rotting food.
Interestingly, Rhizopus stolonifer can also be of use to humans; it is actually used for medicinal purposes in contraceptive pills and can transform steroid hormones, such as progesterone, in order to treat individuals who have hormone deficiencies.
A second common type of bread mold is NeurosporaCrassa, which was discovered in 1843 when it infested a large number of bakeries in France. The name means "nerve spore", and the mold is a member of the filamentous fungi family.