The International Gay & Lesbian Human Rights Commission
IGLHRC's mission is to protect and advance the human rights of all people and communities subject to discrimination or abuse on the basis of sexual orientation, gender identity or HIV status. Since they have contacts in many countries they can help with asylum cases.
The Lesbian & Gay Immigration Rights Task Force (LGIRTF)
An organization that deals exclusively with immigration rights:
Vermont Civil Unions? We don't know yet what effect Vermont's new law will have on immigration rights. A case would have to be brought because the Federal DOMA would have to be challenged and because the law grants "civil unions" rather than "marriage," and civil unions have no precedent in federal law. For more information on the Vermont laws see my Marriage Page.