I see that most people have a difference in opinion for this advice, and it makes perfect logical sense.
OF COURSE being gay shouldn't matter. OF COURSE it shouldn't keep anyone one. OF COURSE being gay makes you unique, and OF COURSE we should have more gay doctors.
But it's also important to realize that we don't live in an ideal world, where interviews, decisions, or even elections are decided on impressions and not pure logic. (There have been studies done on this, and actually they talked about this on Brain Games on National Geographic last night, which is an AWESOME show, but I digress). Many interviews are a generation older, so mentioning your sexual orientation may not leave an optimal impression for them. (Again, we don't live in an ideal world).
Postalkwk mentioned acting as an EC, and how that seems unrelated to being a doctor. This is true, but almost every person would agree that medical school is challenging, and it's crucial to have ECs in order to have a balanced lifestyle. This is why you fill medical schools care so much about your ECs. It's not like they just want to hear interesting stories from applicants all day. From this angle, can you see how being gay or straight is a little different from ECs in interviews?
A common question asked on interviews is "How can you contribute to the diversity of our school?" And OF COURSE being gay makes you unique, but just saying "Well, I'm gay and married" is not a good answer, just like how "I'm Asian" or "I'm black" are awful answers.
If you want to make it relevant, talk about your struggles, and how that made you more compassionate and understanding. Or talk about your volunteering experiences with the LBGT community. Don't just briefly mention that you're in a gay marriage, just because.
Final note: Some schools/areas are more liberal than others. Keep this in mind when you go into your interviews.