US Libertarian Party. Awesome group of people.
Issues that are relevant and important to a particular community. A good example of this is affirmative action. Women and racial minorities are more likely to perceive it as worthwhile and important than white men are. Gay people are generally more interested in seeing civil unions or gay marriage legally respected by the government, straight people might care, but the incidence of straight people who are very much for that cause is quite low proportionally compared to the number of gay people for it. For the deaf community, access to education in ASL is an example of something most people who are deaf or hard of hearing want available, regardless of whether or not it's their preferred way of communicating.
The Dems take advantage of these groups of people by catering their political philosophy to the sigma of the views on specific "community issues" represented by such groups of people. They get support from those groups in the form of campaign contributions and votes.
There is nothing about most of these groups that makes them inherently Democrats or Republicans--Democrat and Republican are just political parties, labels people brand themselves with. People will often vote for the political party they think best represents their views, and for minorities and Generations x and Y women, that party is the Dems.
Libertarian Party, hint hint.