We often like to think our country is founded on the idea that all people are created equal. This of course is actually just a nice line from the Declaration of Independence, and the idea is not necessarily echoed in the Constitution, at least not as explicitly. That technicality aside, I think it is a good starting point for a republic to admit that everyone in the society is equal under the law (think Magna Carta, but for everybody).
Today a Californian judge actually thought this through and came to an obvious decision: it goes against the California constitution to ban same-sex marriage. Here's a link to the NYTimes.com article: The New York Times > National > California Court Rules Same-Sex Marriage Ban Unconstitutional