Min bets not on the river are usually weak. A lot of times it's a hand that the person just doesn't want to lay down, so they are making a "blocking" bet. This can be AK that missed, or often top pair, no kicker.
A lot of times you will raise these bets, they will call, and then min. bet into you on the turn again!!
You have to be careful in these situations, because a lot of these players intend to call you down no matter what, you can't get them to fold their "made" hand (or their "pretty" preflop hand).
When someone min bets from early position into a multiway raised flop I just treat it like they checked: call if I was going to check, put in my standard continuation bet if I was going to make one, etc.