A relatively recent article by Dr. Tzvi Zohar in Akdamot has seemingly raised the whole pilagshut (concubinage) issue again, but, really, people have been talking about it for a while, now. Hirhurim notes a few other sources (and rebuttals), and I’m pretty sure R. Arthur Waskow was supporting this notion as a replacement for kiddushin a while back as well.
In short, a pilagesh is a woman permitted to sleep with a man, and (see Sanhedrin 21a) there’s no ketubah and no kiddushin involved. With no contract and no responsibility, there’s also no certainty of duration–the encounter can be for a night or a lifetime. The only thing that makes it “kosher” is that the woman can’t be in niddah (a state of menstrual “impurity”) and has to go to the mikveh after niddah and before intimate relations.
For some people, perhaps, there’s interest in making up an offical “pilgashut” agreement, wherein the woman becomes the pilegesh of the man, in lieu of kiddushin or its variations.
ADVANTAGES: Nobody gets bought, there’s no get issue, it’s a way of putting very modern idea into an ancient Jewish framework, it’s a way of giving a ritual a Jewish flavor if one primarily wants a civil/secular, rather than halakhic marriage.
DISADVANTAGES: There’s no ritual/legal binding, nobody is responsible or obligated to anyone else (which, at least to me, gives the thing a lot less weight and meaning, but I suppose others might see this as a pro), setting this up in a ritualized way is almost superfluous, since the whole point of pilagshut is that you don’t need the bells, whistles and contracts.