Dragonball Z yaoi is a
sub-fandom of
DBZ fans who are interested in sexual or romantic relationships between the male characters.
Yaoi is a genre for women analogous to girl-on-girl erotica for men; no one ever questions what the appeal for seeing two chicks get it on is for a guy. After all
what's good for the goose is good for the gander. A very informative article on the appeal of
slash can be found in Wired News at http://www.wired.com/news/culture/0,1284,38484,00.html
As a generalization, characters in yaoi are often extremely feminine. While some doujinshi portray the characters as slender and feminized, DBZ yaoi fans are something of an oddity in the yaoi community in that the men are heavily-muscled warriors & fighters. Thus DBZ yaoi is a genre between genres - shunned by purists who feel the concept of Goku and Vegeta having gay sex is an insult to all they hold dear, and unappealing to the general yaoi community for being too masculine.
Indisputably the most popular pairing is Goku x Vegeta, with the prince usually being the uke. However American fans are much more flexible about this than Japanese - wherin, culturally, the seme/uke relationship is often determined strictly by height rather than personality - so Vegeta gets a fair share of seme action from American authors & artists. Other popular pairings are Piccolo/Gohan, Trunks/Gohan, and Trunks/Goten. Vegeta/Trunks, Trunks/Goku, Vegeta/Goten, Vegeta/Yamucha, and Vegeta/Gohan pairings all have their audiences as well. It does seem that Vegeta, being the fangirl's favorite, gets the lion's share of the action.
Being an alien race, the potential for bestowing Saiyajins with many animalistic qualities is rarely passed up. However, these qualities are usually more catlike (purring, growling, etc) than anything else. There is also a tradition of Saiyajin mating rituals that have sprung up among the American fanfic communities.
For one, the Saiyajin tail (or tail spot that is left from the amputation) is almost unanimously classified as an erogenous zone. In the canon, most Saiyajins can be rendered powerless by grasping their tail (why this is is left unexplained, although it is hinted that it causes them extreme pain). This definitely applied to Radditz and Goku (although I have heard that in later episodes of Dragonball he went through training to overcome this weakness). Nappa, however, was immune. Vegeta's tail was never subjected to such treatment so speculation about his tail abounds. Saiyajins loose the ability to go oozaru (their giant ape form) when their tail is cut off, so by the middle of Dragonball Z there are no intact Saiyajins remaining due to the danger posed by this transformation. Being immensely popular with fans of the Saiyajin race, however, tails are often wished back with the Dragonballs or regenerated (both Goku and Gohan's tails grow back several times when they are children) within yaoi/shounen-ai fanfics.
Another strong fan tradition is The Claim Bite. This has absolutely no basis in canon; however, it might as well be fan canon. Saiyajins are supposed to mark their chosen mate with a bite to the neck, the slightly larger & sharper carnassials of Saiyajin enabling them to break the skin and leave a scar. Usually the ritual involves tasting or drinking the bitten's blood. Blood is also often portrayed as something of an aphrodisiac for Saiyajins - being the "ultimate warrior race" with a passion for battle, one can see how authors would come to this conclusion. The vampiric roots of the claim bite are quite obvious; neck sensuality and gothic romance undertones both contribute to the proliferation of this tradition.
A telepathic bond is sometimes created between mates; it occasionally preceeds, but often is initiated with the claim bite.
Nigh-universal is the idea that Frieza sexually abused Vegeta. This gives authors lots of potential for angst, as well as for his partner (usually Goku) to do some serious therapy/emotional healing work. The theory is fed by the particularly sadistic way in which Freeza kills Vegeta on Planet Namek.
Somewhat less prolific but with enough of a presence to warrant a mention is the Hunt. Sometimes cultural, sometimes instinctual, the dominant partner will "hunt" their chosen mate, subdue them (usually through battle) and claim them (usually with a bite).
Numerous authors have also speculated a Saiyajin heat/rut cycle, the possibility of male pregnancy, the havoc a half-formed bond can wreak, and undoubtedly others I have neglected to mention. Of course, if you're interested, hie thee to a search engine & dig it up yourself!