What happens in the endgame Rook + Knight vs Rook? Is it a draw, or can the side with the knight win? I came across this a few days ago, and I managed to win with the Rook + Knight, but I am not sure if that is just because my opponent made a mistake.
Like its cousin endgame KRBvKR, your ending of KRNvKR is usually drawn. It's not always drawn, of course, but generally speaking KRNvKR is much less dangerous and easier to defend than is KRBvKR. In Secrets of Pawnless Endings, John Nunn writes,
If the defending king is not in a corner there are a few situations when the rook and knight can win tactically within a few moves, usually by a combination of skewer and knight fork, but in general the rook and knight only have winning chances when the defender's king is very badly placed.
The positions of KRNvKR are a part of existing tablebases, so we can be precise about how often it's a win: 35.9% of positions in which the strong side has the move are winning (see e.g. Ken Thompson's "Retrograde analysis of certain endgames" from 1986). Note that since that says that giving the strong side the move (which is advantageous most of the time) in a random position yields a win only 35.9% of the time, the overall winning percentage for the strong side in KRNvKR is considerably lower than that; I am unable to pin the figure down from any source so far.
For your particular game, Nunn's words can give some inkling as to whether your opponent made a mistake or was already doomed, but if tablebases have taught us anything it's that optimal play can be quite seemingly random, and that heuristics are of limited use for a reliable verdict. If you have a record of the initial KRNvKR position that appeared on the board in your game, though, then a quick Nalimov tablebase query will tell you whether or not your opponent sealed his fate during that ending or before it.
It is usually a draw, but some positions are winning, which can take up to 33 moves to convert. A complete mastery is shown at http://www.youtube.com/watch?v=m-OlC-evq28
Search for a game of Cuban GM Leinier Dominguez, after many moves he won the game and it was vs another GM, I just don't remember the opponent. I thought this will be a draw until I saw this game. I don't remember the opponents king to be in a bad position.
It seems to be this game: http://www.chessgames.com/perl/chessgame?gid=1499346