I bought my 2003 325iT recently and have been working on it (Dr. gives a general checkup). I pulled out the back seat and checked if the fuel pump had been replaced. It was based on the evident.
Here is one way to check if the pump is near end of its life: turn on the dash hidden on-board display to show both fuel tanks capacity. If the right tank is much less than the left then time to change the pump as when it running weak it couldn't pull the fuel from left tank to the right tank leading to engine ran out of fuel while there is plenty of fuel in the left tank.
Here is one way to check if the pump is near end of its life: turn on the dash hidden on-board display to show both fuel tanks capacity. If the right tank is much less than the left then time to change the pump as when it running weak it couldn't pull the fuel from left tank to the right tank leading to engine ran out of fuel while there is plenty of fuel in the left tank.