Since I don't have much to add today, I'll just leave you guys with a trope. If you have any questions, don't hesitate to ask.
"I don't have a wife. Zoe, why do I have a wife?"— Malcolm Reynolds, Firefly episode "Our Mrs. Reynolds."
Be careful when visiting foreign parts or in the company of aliens, because you never know... you just might end up married. A character (almost always a male) discovers that a seemingly innocent action now entitles him to a permanent fashion accessory — an intense young lady who insists that they are now married. Sometimes it's a delusion on her part, but sometimes it's valid — at least by the rules of the place where she grew up.
Naturally, this never happens to someone who would be willing to just walk away and leave her stranded. Or, for that matter, to someone who's willing to bite the bullet, settle down with their accidental bride, and have two and a half accidental children.
When set in modern times, the possibility of the marriage being real is usually set up by the officiant being a legitimate minister or justice of the peace.
As to the real-life possibility of an Accidental Marriage being valid (at least in North America), it's pretty remote: although courts in both the U.S. and Canada have decreed that a couple who thinks they're legally married is legally married, at the same time a marriage usually isn't considered valid without a marriage license, which has to be purchased before the wedding (and in most places both parties to the wedding have to buy the license together). This was originally meant to prevent marriage fraud, but it also allows the state or provincial government to make a little money on each ceremony.
Additionally, the "getting drunk and waking up married" type is not valid either, since the law requires that both parties enter into the relationship voluntarily and in full possession of their faculties. (This is nearly always in Las Vegas in the US version, due to the fact that unlike many states Nevada does not require a waiting period between obtaining the license and the marriage itself, and that the Clark County marriage bureau office in Las Vegas is open until midnight every day of the year, even weekends and holidays.)