For different-sex married couples, it is usually possible for the couple to divorce where they are currently living regardless of where they originally married. The reason for this is that for the most part, states respect the marriages of different-sex couples regardless of where the couple married. If a place respects the marriage, provided the couple meets the divorce residency requirements in that locale, they will be allowed to divorce where they currently live.
The complication for same-sex couples is that only certain places respect the marriages or civil unions of same-sex couples, and so you need to live in one of those places to be able to dissolve the relationship.
If you have a same-sex marriage, regardless of where you married, you will be able to dissolve it in places where same-sex couples can legally marry (i.e. MA, CT, NH, VT, IA, DC, NY), provided you meet the residency requirements for that place's divorce law. There may also be some additional states that, although they do not allow same-sex couples to marry, do respect the marriages of same-sex couple, at least for the purpose of divorce.
For couples in civil unions, the civil union can be dissolved in any state that had a civil union at some point, even though they may not now offer civil unions (i.e. VT, CT, NH, NJ, RI, IL and, effective January 1, 2012, DE and HI). Also states with domestic partnerships that offer nearly all the benefits of marriage like CA, OR, WA and NV also will likely dissolve a civil union. In addition, even places that offer marriage for same-sex couples may be willing to dissolve civil unions as well, but possibly using a legal procedure different from divorce (e.g. MA has dissolved civil unions under equity law). However, in all of the above, you will most likely still need to satisfy a residency requirement before the state has jurisdiction to dissolve your civil union.
For either ending a marriage or a civil union it only takes one member of the couple to file for the dissolution of the relationship, and so only one member of the couple needs to live in a place that respects the relationship, and only one member of the couple needs to meet the residency requirement for ending the relationship.
Although this seems (and is) rather complex, the bottom line is that if you wish to end either a marriage or a civil union don’t assume that the only way to do it is to return to the place where you entered into it. If you live in one of the New England states, contact GLAD’s Legal InfoLine at 800-455-4523 to find out about your options, and, if you live outside New England, contact Lambda Legal (go to www.lambdalegal.org to see the contact information for their regional offices).