This is a complicated question which defies a simple answer. I might start by saying that multiple pawn exchanges tend to open up the game, and this can lead to lots of piece exchanges and a quiet, "drawish" position which is hard to get excited about.
Consider the "Exchange French," for instance: 1 e4 e6 2 d4 d5 3 exd5 exd5. After this exchange of central pawns, the king file is open. The control of an open file is a strategic asset. Therefore, players will fight over the control of this territory by lining up their queens and rooks on the open file. This tends to lead to an exchange of these "heavy pieces." After a lot of pieces have left the board, it's hard to whip up an attack; instead, you're often left hoping your opponent makes a mistake.
Every exchange of pieces should have a point; every exchange of pawns should be considered just as carefully. Remember, as one grandmaster once put it, that chess is not checkers--captures are not mandatory!
This is a puzzling difference I notice between the games I play and the games of good players.
In my games, pawns that are "in the firing line" - i.e. in a position in which another pawn can take them are almost always exchanged, whereas good players seem to often leave them there for ages without taking.
Why is this?