The Bible doesn't have a lot to say about same-sex intercourse, but what is there does seem on the surface hard to reconcile with gay relationships that involve sex. It is important to note that two gay persons could still have a romantic relationship, even live together, without sex, and there is no condemnation of this in scripture or tradition.
I find certain passages such as the Sodom and Gomorrah story inadequate to condemn homosexuality. The prophets and Jesus denounced the sin of Sodom as inhospitality. Because the angels, thought to be men, were given refuge they were not to be harmed, but the men tried to rape them anyway. So far as I know there are strains of thought within Jewish tradition that did condemn the sin of sodom as homosexual acts, although this interpretation only arose fairly late in Christian tradition. Romans 1 is also interesting. Many early church fathers interpreted these acts to refer to sex during menstruation which was condemned not as a mere purity taboo but as an act of injustice in Ezekiel 18. Indeed the early church fathers condemned sex during menstruation across the board, though they differed as to whether these sins were venial or mortal. The Catholic Church no longer teaches this.
It is important to consider why Jewish and Christian tradition looked on sex between two persons of the same sex as so heinous. The Jewish scriptures don't actually mention sex between two females. The only passage used as a reference to female homosexuality is Romans 1 which is not how early fathers interpreted it. Sex between two women did not involve penetration and did not involve making one man "act as the woman," which in Jewish patriarchal culture was a debasement to a man. In cultures surrounding Jewish and Christian thinkers male-male sex was often rape, an act of humiliating another, often times in war. Other times it involved prostitution, particularly involving pagan gods, or the enslavement of young boys as sex slaves. Given that context for homosexuality it would naturally be condemned. Homosexuality in our modern culture generally involves people who are in loving relationships, relationships that often involve great sacrifice in the face of hostility. Most often gay sex does not involve slavery, prostitution, or cultic prostitution. It is worth considering whether our very different context for homosexuality warrants a re-evaluation of the tradition. Also worth considering is other ways that Christian teaching (by which I mainly refer to Catholic tradition which I am most familiar with) has developed in regard to sex.
Much of the condemnation of homosexuality in Catholicism today involves natural law theory, the same sorts of ideas that prohibit masturbation and contraception as intrinsically evil acts, that prevents an impotent man from marrying, or any person who has a deformity such that (s)he cannot participate in vaginal intercourse culminating in ejaculation within the woman. I find many of these arguments dubious at best, as do even some theologians who accept the traditional moral teachings.
You might find these articles interesting. I can't vouch for everything in them mind you, but I am in general sympathy with the ideas contained therein. They concern homosexuality and contraception from the point of view of a man who identifies as a gay (and partnered) traditonalist Catholic:
Faithful to the Truth: The Testimony of Sacred Tradition.
Pharsea: Contraception.