Knight or 3 Pawns?

Which would you prefer? And in what circumstances

Many factors. If there is a lot of other material on the board and the 3 pawns are not close to queening or passed then maybe the knight. But the less material left the more I would prefer the pawns, especially if they are connected and passed. If its purely king + knight vs king + 3 pawns then definitely the pawns, even if they are not connected. The knight is not good at stopping pawns with its limited range compared to a rook or a bishop.

3 pawns = 3 potential Queens. Just saying.

Exactly.

I'll take 3 pawns on a, d, and h file against a knight. I played it before and queened one of them. 

8 pawns BY FAR.

Maybe you would like to reconsider that? White wins in that diagram...

I see your dirty trick...unfortunately, the wording 1. Ne3 in the solution spoils everything, since this suggests the moving direction of the Black pawns.

Depends on the situation (like Strangemover suggested). Imagine the situation where the three pawns are tripled. Or imagine another situation where the three pawns are all near the promotion squares. I have been on sides with the piece but less pawns, and I have also been on sides with a piece deficit for pawns, and different situations favour different sides. But my personal preference is the pawns - even just two pawns for a piece is good enough.

Generally speaking, a minor piece is better than three pawns unless the pawns are fairly advanced.

You can always find exceptions, but that's a pretty reliable general rule.

A lone knight can't win, but 3 pawns definitely can. 3 pawns no question

It all depends on the position 

Yep!

Middlegame: knight

Endgame: 3 pawns

As Sherlock would say, the direction is already clear.

on one tournament once i had 4 pawns (h,g,f,d) against knight, there were rooks too and my opponent had one pawn e or f i do not remember. i could not win. once this knight starts jumping all over the board that is worst thing you might get in one chess game...