Sorry, I know its unconventional to post 2 hands in the same thread, but these hands happened against the same player and both times he does the same thing. Call, call, call, bet?!??

Hand #1:
Party Poker 2/4 Hold'em (9 handed) FTR converter on zerodivide.cx

Preflop: Hero is CO with 6:spade:, 6:heart:.
UTG calls, 4 folds, BB checks.

Flop: (4.50 SB) T:spade:, 3:club:, 4:club: (4 players)
BB checks, UTG checks, Hero bets, Button folds, BB calls, UTG calls.

Turn: (3.75 BB) 5:diamond: (3 players)
BB checks, UTG checks, Hero bets, BB calls, UTG folds.

River: (5.75 BB) K:diamond: (2 players)
BB bets, Hero?

Hand #2:
Party Poker 2/4 Hold'em (9 handed) FTR converter on zerodivide.cx

Preflop: Hero is CO with J:diamond:, J:heart:.
5 folds, BB calls.

Flop: (4.50 SB) T:diamond:, 3:heart:, 4:spade: (2 players)
BB checks, Hero bets, BB calls.

Turn: (3.25 BB) 2:club: (2 players)
BB checks, Hero bets, BB calls.

River: (5.25 BB) A:spade: (2 players)
BB bets, Hero?

Call and call, and take note of whether he was bluffing, or had a hand, etc.

I like Zach's idea with calling both hands.

The river donkbet can sometimes be a very key part of someone's game, and I've notived that these habits tend to not fluctuate with most players.

Even if calling is somewhat borderline on the first hand, I think the BB you spend for information (in addition to you possibly having the best hand) will either save/make you a net profit when this situation arises again later on in your session.

The simple answer is, you basically always have to pay bets like this off in mid-sized and larger pots with your made hands against almost all opponents.