A mummy is a general term for any corpse that has been preserved from decay, usually through drying but sometimes through chemical means.
Ice Mummies
Mummies can form naturally in cold, dry environments such as mountain peaks and in glaciers. (If you've ever found a poorly-wrapped steak that's been in the freezer for a really long time, you can easily see how flesh can dry out through sublimation even though it's surrounded by ice). The most famous recent example of a high-altitude mummy discovery is "The Iceman", the Bronze Age corpse that was discovered remarkably preserved in the Ötztal Alps by a mountaineering team in 1991.
However, many more "ice" mummies have been recovered from the mountains of Peru. The Incas drugged and sacrificed children to their mountain gods high in the Andes over 500 years ago. The children were left to freeze to death with gold and other valuables. (Other Incan mummies have been found in underground caverns, their bodies preserved by the high salt content of the soil.)
Mummies have also been found in the mountains and permafrost of Siberia. One such famous mummy is the "Siberian Ice Maiden", who was discovered in the High Steppes. She is believed to have been a priestess of the lost Pazyryk culture. She died about 2400 years ago; her body was frozen and mummified by the unusual climactic conditions of the period.
Mud Mummies
The Chinchocos, a tribe that was probably ancestral to the Incas, mummified their dead as long ago as 5000 B.C. This tribe lived in what is today the border of Peru and Chile and they mainly survived through fishing.
To preserve their corpses, they would completely take apart the body, dry the flesh and organs in the sun or over a low fire, then put the body back together. They used sticks to reinforce the spine and the limbs, and they used clay, feathers and grass to pack everything in. They would coat the body in ash, create a mask out of dried mud, adorn the body with a wig, and then paint it in black manganese or red ochre pigments, depending on the period.
Bog Mummies
About 1500 mummies have been pulled from peat bogs in Northern Europe. All these mummifications occured naturally because of the tannic acids, lack of oxygen, and cold temperatures of the water in the bogs. Some of the people fell into the bogs accidentally; on the surface, the bogs can look like solid ground, but the mossy surface covers deep water. However, most bog mummies were ancient sacrifices, suicides, or murder victims. The bodies are usually quite well-preserved, and the skin has a dark, leathery look.
The best-known bog mummy is the Tollund Man, who is on display at the Silkeborg Museum in Denmark. The Tollund Man was strangled to death with a leather cord sometime in the Iron Age; his corpse was discovered by two brothers digging for peat in 1950.
Another well-known bog mummy is the Lindow Man (see that node for extensive information).
Florida's swamps also have a preservative effect on some corpses; several very old skeletons have been pulled from Floridian bogs with their brains still intact.
Sand Mummies
The mummies of Egypt are, of course, the most famous mummies because they are so plentiful. However, mummies form in almost every desert environment and they've been pulled from the sand throughout Northern Africa and the Middle East. Caucasian mummies have been found in the Tarim Basin and in the Takla Maken Desert in China; these mummies died about 1000 B.C. and have provoked much speculation about who they were and where they came from.
Egyptian Mummies
The naturally-forming mummies no doubt gave the ancient Egyptians the idea to take the process even further to preserve their corpses for a rich afterlife. They believed that the soul re-entered the body after death, so it was necessary to preserve the body. The Egyptians started artificially mummifying corpses at about 2600 BC; the practice ended at approximately 600 AD.
The Egyptians mummified corpses on a huge scale, and they didn't just do people. Followers of the ancient Egyptian religions created cemeteries for embalmed creatures sacred to their gods: cats, monkeys, crocodiles, and ibises were common mummy animals.
The Egyptians originally used asphalt as the main ingredient for mummification, but over the millenia they turned mummification into a complex procedure.
The whole process of mummifying a body took 70 days. First, they would remove the brain and the intestines, which they put into separate vessels called canopic jars. They'd pull the brain out through the nose or the eye cavity with a hooklike instrument. Next, the body would be washed in palm wine and rubbed with incense. The embalmers would dessicate the body tissues with a liberal application of soda. After the body was suitably dried out, the embalmers would fill the cavity with stuff like sawdust, linen, mud, lichens, and resinous oils to preserve its shape. They would coat the body with beeswax, pine resins, asphalt, and gum arabic as they wrapped it in linen bandages. They sometimes painted a face on the linens, and sometimes they'd shape breasts or genitals on the finished mummy.
Uses of Egyptian Mummies
Because of the huge quantities of mummies lying around in the sands of Egypt, European and Egyptian entrepreneurs alike figured out ways to make money off them (aside from plundering the tombs, of course).
Mummy Medicine
In the Renaissance, a thriving trade in mummy parts to Europe started. Supposedly, powdered mummy flesh or the resins from mummies would work as an aphrodisiac or as a cure for all manner of ailments. This use of mummies as medicine continued for centuries.
From the 1771 edition of Encyclopaedia Britannica:
We have two different substances preserved for medicinal use under the name of mummy, though both are in some degree of the same origin. The first one is the dried and preserved flesh of human bodies, embalmed with myrrh and spices; the other is the liquor running from such mummies, when newly prepared, or when affected by great heat or damps. The latter is sometimes in a liquid, sometimes of a solid form, as it is preserved in vials well stopped, or suffered to dry and harden in the air. The first kind of mummy is brought to us in large pieces, of a lax and friable texture, light and spungy, of a blackish brown colour, and often damp and clammy on the surface: it is of a strong but not disagreeable smell. The second kind of mummy, in its liquid state, is a thick, opaque, and viscous fluid, of a blackish colour, but not disagreeable smell. In its indurated state, it is a dry solid substance of a fine shining black colour, and close texture, easily broken. and of good smell; very inflammable, and yielding a scent of myrrh and aromatic ingredients while burning.
This, if we cannot be content without medicines from our own bodies, ought to be the mummy used in the shops; but it is very scarce and dear; while the other is so cheap, that it will always be most in use.
All these kinds of mummy are brought from Egypt. But we are not to imagine that anybody breaks up the real Egyptian mummies, to sell tham in pieces to the druggists, as they may make a much better market of them in Europe whole, when they can contrive to get them. What our druggists are supplied with, is the flesh of executed criminals, or of any other bodies the Jews can get, who fill them with the common bitumen so plentiful in that part of the world; and adding a little aloes, and two or three other cheap ingredients, send them to be baked in an oven, till the juices are exhaled, and the embalming matter has penetrated so thoroughly that the flesh will keep and bear transporting into Europe. Mummy has been esteemed resolvent and balsamic: but whatever virtues have been attributed to it, seem to be such as depend more upon the ingredients used in preparing the flesh, than in the flesh itself; and it would surely be better to give those ingredients without so shocking an addition.
Mummies as Fuel
As you can gather from the above paragraphs, mummies burn quite well (and, apparently, smell better than you'd expect). And in the 1800s when steam locomotives came to Egypt, mummies were more plentiful than trees or coal. So, for many years, the Egyptian railway between Cairo and Khartoum was fueled almost entirely with mummies of whatever sort they could pull from the sand.
Reference:
Encyclopaedia Britannica (1771)
The Man in the Ice by Konrad Spindler
http://library.thinkquest.org/J003409/