[Nick C]

I probably call and see what Villain wants to do on the turn.

Villain most likely either has a monster (an overpair or better) or has a marginal made hand or a draw. With the latter possibilities, he'll often slow down on the turn.

Which sucks for you when what he has is a draw, but these min-raises are big hands often enough that I probably would shut down here. This allows an unknown to make an effective cheap-draw/cheap-showdown play if that's what he's doing, but what can you do? I don't think you really want to play for stacks, and the popularity of the min-raise as a slowplay sort of provides cover for Villain if he's doing something else instead.

And, having said all of that, I should add that what is often going to happen next is that Villain will follow up with smallish bets that will string you along, but you're not always going to lose at showdown at the end of those small bets.