Yes. As of July 2013, same-sex marriage is legal in 13 states and the District of Columbia. Same-sex couples can now marry in California, Connecticut, Delaware, D.C., Iowa, Maine, Maryland, Massachusetts, Minnesota, New Hampshire, New York, Rhode Island, Vermont and Washington.
Many other states have passed laws specifically barring same-sex marriages. However, there are states that allow same-sex unions called "civil unions" or "domestic partnerships" that are similar to marriage and offer all or most of the benefits married couples receive.
Colorado, Hawaii, Illinois and New Jersey offer civil unions. Delaware, Rhode Island, Vermont, New Hampshire and Connecticut had civil unions, but with the legalization of same-sex marriage in each of these states, valid civil unions have been (or will be) merged or converted into marriages.
California, Oregon, Washington, Maine, Hawaii, D.C., and Nevada offer domestic partnerships. Rights and benefits for couples in domestic partnerships vary from state to state. Wisconsin offers a type of domestic partnership, but it's more akin to a registration for same-sex couples, which confers limited spousal rights.
If you are in a registered domestic partnership in California, the recent ruling legalizing same-sex marraige has no effect on your relationship status. Domestic partnership registrations are different from marriage licenses. The California Secretary of State’s Office will continue to process domestic partnership registrations and notices of termination of domestic partnerships.
In Washington state, any state registered same-sex domestic partnership, where neither party is sixty-two years of age or older, will be automatically converted into a marriage as of June 30, 2014.
For more information, see Nolo's article Same-Sex Marriage: Developments in the Law. For guidance on whether to enter into a marriage or other legal relationship with your same-sex partner, see Making It Legal: A Guide to Same-Sex Marriage, Domestic Partnerships & Civil Unions, by Frederick Hertz with Emily Doskow (Nolo).