Should the pawn capture towards the center or not?

Another consideration: if White has a pawn on e5 and the possibility of using the g5 square, Black might well want to take on g6 with the f pawn. The reason is that a subsequent ...h6 is less damaging to the Black K position than ...f6, which would allow exf6. Here is an example given by Soltis in "100 Chess Master Trade Secrets":

The details didn't show up in the post: the game is Spassky-Petrosian from their 1969 match.

Very interesting post OldPatzerMike, I was focused on addressing the open file, or not, based on my own chances; however, in this example we see the decision based not on one's own plans - but rather on how to prevent your opponent's plans via counterplay: very interesting indeed.

I agree with scrabblechecs. There is no future for the Black rook on the f-file, and there is no reason to make the backward e-pawn weak.

Generally they should I think as everything is being geared towards the center, the most important 4 squares of the Chessboard but honestly it depends upon the position and what you're trying to do.