In Schalk and Kopf v. Austria, the European Court of Human Rights has rejected an application seeking a right to same-sex marriage within the European Convention on Human Rights. Article 12 of the Convention, which is derived from the Universal Declaration of Human Rights, states: 'Men and women of marriageable age have the right to marry and to found a family, according to the national laws governing the exercise of this right.' The applicants argued that under a dynamic interpretation, this provision should now be read as protecting a right to same-sex marriage. The Chamber said that 'the institution of marriage has undergone major social changes since the adoption of the Convention, the Court notes that there is no European consensus regarding same-sex marriage' (para. 58). Three of the seven judges dissented. According to Judges Rozakis, Spielmann and Jebens, same-sex relationships are accepted by society, and require an adequate legal framework. The absence of such a framework constitutes a violation of articles 8 (right to privacy, family, etc.) and 14 (non-discrimination).
Thanks to Christopher Ryan, who has written about this on his own blog.