Mitochondrial DNA (mtDNA)
 

The human mitochondrion contains 5–10 identical, circular molecules of DNA. Each consists of 16,569 base pairs carrying the information for 37 genes which encode:
 

2 different molecules of ribosomal RNA (rRNA)
22 different molecules of transfer RNA (tRNA) (at least one for each amino acid)
13 polypeptides
The rRNA and tRNA molecules are used in the machinery that synthesizes the 13 polypeptides.
 

The 13 polypeptides participate in building several protein complexes embedded in the inner mitochondrial membrane.
7 subunits that make up the mitochondrial NADH dehydrogenase
3 subunits of cytochrome c oxidase
2 subunits of ATP synthase
cytochrome b
Each of these protein complexes also requires subunits that are encoded by nuclear genes, synthesized in the cytosol, and imported from the cytosol into the mitochondrion. Nuclear genes also encode ~900 other proteins that must be imported into the mitochondrion. [More]
 

Mutations in mtDNA cause human diseases.
A number of human diseases are caused by mutations in genes in our mitochondria:
cytochrome b
12S rRNA
ATP synthase
subunits of NADH dehydrogenase
several tRNA genes
Although many different organs may be affected, disorders of the muscles and brain are the most common. Perhaps this reflects the great demand for energy of both these organs. (Although representing only ~2% of our body weight, the brain consumes ~20% of the energy produced when we are at rest.)
 

Some of these disorders are inherited in the germline. In every case, the mutant gene is received from the mother because none of the mitochondria in sperm survives in the fertilized egg. Other disorders are somatic; that is, the mutation occurs in the somatic tissues of the individual.
 

Example: exercise intolerance
A number of humans who suffer from easily-fatigued muscles turn out to have a mutations in their cytochrome b gene. Curiously, only the mitochondria in their muscles have the mutation; the mtDNA of their other tissues is normal. Presumably, very early in their embryonic development, a mutation occurred in a cytochrome b gene in the mitochondrion of a cell destined to produce their muscles.
 

The severity of mitochondrial diseases varies greatly. The reason for this is probably the extensive mixing of mutant DNA and normal DNA in the mitochondria as they fuse with one another. A mixture of both is called heteroplasmy. The higher the ratio of mutant to normal, the greater the severity of the disease. In fact by chance alone, cells can on occasion end up with all their mitochondria carrying all-mutant genomes — a condition called homoplasmy (a phenomenon resembling genetic drift).
 

Why do mitochondria have their own genome?
Many of the features of the mitochondrial genetic system resemble those found in bacteria. This has strengthened the theory that mitochondria are the evolutionary descendants of a bacterium that established an endosymbiotic relationship with the ancestors of eukaryotic cells early in the history of life on earth. However, many of the genes needed for mitochondrial function have since moved to the nuclear genome.