The most common types of pseudogenes are processed pseudogenes and those derived from gene duplication events [duplicated pseudogenes].
The third type of pseudogene is the "unitary" pseudogene. Unitary pseudogenes are genes that have no parent gene. There is no functional gene in the genome that's related to the pseudogene.
Unitary psedogenes arise when a normally functional gene becomes inactivated by mutation and the loss of function is not detrimental to the organism. Thus, the mutated, inactive, gene can become fixed in the population by random genetic drift.
The classic example is the gene for L-glucono-γ-lactone oxidase (GULO), a key enzyme in the synthesis of vitamin C (L-ascorbate, ascorbic acid). This gene is functional in most vertebrate species because vitamin C is required as a cofactor in several metabolic reactions; notably, the processing of collagen [Vitamin C]. This gene has become inactive in primates so primates cannot synthesize Vitamin C and must obtain it from the food they eat.
A pseudogene can be found at the locus for the L-glucono-γ-lactone oxidase gene[GULOP = GULO Pseudogene]. It is a highly degenerative pseudogene with multiple mutations and deletions [Human GULOP Pseudogene]
This is a unitary pseudogene. Unitary pseudogenes are rare compared to processed pseudogenes and duplicated pseudogenes but they are distinct because they are not derived from an existing, functional, parent gene.
Note: Intelligent design creationists will go to great lengths to discredit junk DNA. They will even attempt to prove that the GULO pseudogene is actually functional. Jonathan Wells devoted an entire chapter in The Myth of Junk DNA to challenging the idea that the GULO pseudogene is actually a pseudogene. A few years ago, Jonathan McLatchie proposed a mechanism for creating a functional enzyme from the bits and pieces of the human GULOP pseudogene but that proved embarrasing and he retracted [How IDiots Would Activate the GULO Pseudogene] Although some scientists are skeptical about the functionality of some pseudogenes, they all accept the evidence showing that most psuedogenes are nonfunctional.