• LDS.org: Homosexuality (Same Sex Attraction) — a library of information
• LDS.org: Same Gender Attraction — an interview with Elder Dallin H. Oaks and Elder Wickman
• Ask Gramps: What is the Mormon church’s position toward transgendered persons and gay marriages?
• Ask Gramps: How can I overcome same sex attraction to become a faithful Mormon?
• Ask Gramps: Science and Sexual Orientation
• Evergreen International — a non-profit organization that helps people who want to overcome homosexual behavior.
• Superchastity — an interesting idea to change the semantics of homosexuality in the Church and improve understanding and kindness

The Church rarely takes a position on political issues, except in some family and societal matters, which makes this recent letter all the more interesting. In fact the Church has a policy of being politically neutral:

In this election year, we urge Church members to register to vote, to study the issues and candidates carefully and prayerfully, and then vote for those they believe will most nearly carry out their ideas of good government. Latter-day Saints are under special obligation to seek out and then uphold leaders who will act with integrity and are ‘wise,’ ‘good,’ and ‘honest,’ (see Doctrine and Covenants 98:10). (LDS.org)

The Mormon church’s position on homosexuality is that it’s a behavior and as such can be overcome. I don’t think this denies the possibility that gays may have a biological tendency toward homosexuality, making it difficult to overcome for some. I tend to look at it like a person of Irish descent saying (and I have heard this), “I’m Irish; I have a temper. That’s just the way I am.” No doubt there are tendencies toward certain temperaments, but that doesn’t mean we can’t overcome our tendencies.

FYI, Evergreen International helps gay Mormons overcome homosexuality.

See the following searches at LDSsearch.com for more information:
Gay Mormons
Gays and the Mormon church