Never Give Up!
Premature draw agreements and resignations bother me. Sure, there's a place for agreeing to a draw, and resigning in hopeless situations. But some players do it too soon. Especially at lower-rated levels, it's probably almost never correct to resign early -- there are too many possibilities for your opponent to make a mistake. Why should you punish yourself for making a mistake early in the game and not punish your opponent for making a mistake late in the game?
With that in mind, here's a game I played in 1986, my 23rd rated USCF game, against John Weninger (1642). I lost a piece in the middlegame against an opponent rated almost 150 points higher than me, but I didn't give up. I didn't even have any positional compensation for the lost piece. I just thought I could play well enough in the endgame to force a draw.
After a flurry of trades, we eventually come down to a battle of my 5 pawns versus his 5 pawns and knight. You can skip to move 37 if you want to see that.
So, my opponent made, in my opinion, two mistakes in the endgame that cost him the win. It wasn't much, but it was enough. Even against the extra knight, I didn't give up and was able to hold on for the draw.