A
petition has been started by otaku in Japan for the right to wed 2D characters. Now, the usual jokes like "so ronery" come to mind... but it seems these otaku are really serious about this. Read
the article from my favorite blog for more lulz.
Theoretically it would be impossible since marriage is a joining of two different willing legal entities, and since 2d characters don't have a will...
Not to mention that from a legal standpoint it would have no meaning since these characters don't pay taxes, have to be supported or support anyone, etc.
Edit: To expand on it, this basically means that this type of marriage can not be legally recognized since there is nothing there to legally recognize. Typically when asked to legally recognize a marriage, it means that you are allowed to have joint rights and possessions, as well as visitation rights at hospitals as family. Since 2d characters have no rights (or restrictions for that matter, due to living in a fictitious world) or ability to possess anything outside of that fictitious world, that nullifies the first two. Some how, I don't see any of these characters showing up at a hospital requesting visitation rights as well.