The most important thing to know about moldy bread is that you should not eat it. If mold begins to appear on bread, or most other foods, the food should be discarded and replaced. Much of the structure of mold consists of a mycelium, a delicate network of rootlike structures which can be very difficult to see, which means that even if part of a loaf appears safe to eat, it may be infested with mold.
Some molds that appear on breads are perfectly harmless and safe to eat, but others secrete mycotoxins that can make people sick. Depending on the mold, consuming moldy bread may simply result in a stomach ache, or it could cause more serious health problems. Since identifying molds requires access to a laboratory with a microscope and staining solutions, it's better to simply discard breads which have mold on them, rather than to try and figure out if it is safe. Other foods, like fruits, should also be thrown away if they have begun to mold. The exception to this rule is hard cheese, because the molds that grow on them are usually harmless, so the moldy section can simply be cut off. People who prefer to err on the safe side may want to discard moldy hard cheeses as well.
To slow the rate at which bread molds, you can store it in an airtight container in a cool, dry place. Molds like damp, wet, warm environments, so it's important to make sure that bread has totally cooled after baking to ensure that mold will be less likely develop after it is put into storage. Bread can also be refrigerated or frozen to slow the molding rate.
Homemade, organic, and natural breads tend to become moldy more quickly than commercially produced breads. This is because many bread companies add stabilizers and preservatives to their breads to stave off its growth. The exception to this rule is sourdough, a type of bread that generally does not mold because of the high acidity of the bread.
Bread molds come from a wide variety of genera. Rhizopus stolonifer, or black bread mold, is a type commonly seen in the kitchen, capable of totally covering bread within three days. Some molds are from the Penicillium genus, the same genus used to produce penicillin. If you have access to a laboratory and identification equipment, allowing bread to mold in different environments and identifying the result can be an interesting science project, but be careful. Even when you don't eat it, moldy bread can make you sick if you have a compromised immune system or respiratory problems, as the spores of the mold are free-floating in the air.