Is it ever posible to win if the only pieces left are two kings and a knight? If the only pieces left on the board are the two kings and a knight, is it ever possible to force check mate? I mean, if the bare king avoids the edges and stays close to the opponent's knight, I don't see how the game can ever end. I was in this situation for more than half an hour yesterday and we were forced to draw.
No, it is not possible to checkmate with a lone knight (K+N vs K). 
However, Add another Bishop and you'll be able to Checkmate (K+N+B vs K)

There is a rule in Chess which goes like this "No Mating material = Draw"

So: 

K vs K = Draw

K+N Vs K = Draw

K+B Vs K = Draw