If the King defending against Rook and Pawn can get to the queening square, it should be a draw.  Here is one ending where I had to defend against the extra pawn, but could get to the queening square for a draw. 

Hmm, the 3rd rank / philidor's defense is well known -- perhaps less well known is passive defense on the last rank (see the last position in Bill's diagram after 25...Kb8) is the easiest way to draw against a knight pawn.  I'm not sure why you criticize it eric_c.  The specific defensive set up after black gets in front of the pawn isn't so important here.  I think the instructive part of this deals with how many files the kings are cut off by, and how black works to make sure his king isn't cut off by 4 files in the beginning with his first 2 moves and the notes Bill gives after 2...Re2.

Psychological play also needs to be taken in account.  This was probably a 15 minute game and we were around move 70 with time pressure.  I took the route that I thought I knew best or could play fast enough and not lose on time.  He was a stronger player than me (I am defending a pawn down), and after the game, I could visit the alternative moves.   I may have neglected to state that ...Kf7 drew, but I implied it by listing the only losing moves (Kf8, Kg8, Kh8, Kh7) or just hanging the rook.  All other moves should draw, including Rb2 (or Ra2 through Rh2), and I settled on ...Rg2+ because that's what I saw best to insure the draw.  ...Rb2 may be more efficient, but most players will play what they know best rather than a more elegant, shorter path to drawing (or winning).  Maybe I also thought that White, with some time pressure, could make more of a mistake if my rook was out than hiding behind the passed pawn.  I don't get enough endgame play to know the best lines, but enough to get by.  Its the post-game analysis where you can take some time and find the best moves or use endgame databases or strong engines to find improved play.  I like the comments from everyone and did not think anything was rude or out of line.  I find that most of my endgames are Rook and Pawn endings, but probably less than 2% of my games make it that far.  I continue to study traps and miniatures and hope I can find the right moves when it does come to endgames.  I really can't think of a time I lost a tournament because I lost my games in the endgame.  It is usually the opening or middlegame that decides over 90% or more of my games.  This forum does give me a change to revisit the endgames that I did play.