user3270: When I am introducing beginners to the game, I immediately teach them KQvK, KRvK and KPvK. I follow that up with KBBvK at around the 800 level. Are any resources on when one should learn/teach the following techniques: Lucena win, Philidor draw, KBNvK, KQvKR, KRBvKR, KNNvKP? Each of these teaches valuable lessons with applications beyond just the endgame but the last two may not be worth studying seriously until the IM+ level.

user4418: From teaching my kids I would agree with starting with KQvK and KRvK but I found that the ideas behind KPvK were  a bit too tricky for this level. The opposition and getting the king in front of the pawn were a bit too tricky for beginners. I found KRRvK to be very good not just because it is easy but also because it gives an easy introduction to the "hungry hogs", 2 rooks on the 7th rank. So, KRRvK comes at the same time as the other two basic endings.
Before going for KPvK I would introduce games with just 8Pv8P (no kings), first to get a pawn to the 8th wins, then add kings, same rules. Not being funny but I think this ending comes much later, say at 1200. For Philidor and Lucena I would say around about 1500 or 1600

user3118: This type of question has no real answer, because it is just an opinion... but here goes...
I agree with teaching KQK and KRK immediately. I also usually show KRRK to a new player also. I do this because it is an easy way for them to begin visualizing how the pieces move and control squares, ranks or files. It also shows them how to checkmate the opposing king and the objective of the game without the complexity of 32 pieces on the board. I often show them these mates right after they learn the game.
Except for the Lucena win and Philidor draw, all the others are almost academic unless your a very good player. I don't believe I've ever had to play KQkr or KQkn or KBBk or KBNk in a real game before. At what level do you consistently get to an endgame before someone is lost? I think better players learn them for fun at one point, and they may illustrate some good concepts. e.g. KBNk may show that the N+B work best positioned on the same color squares, but really does that help me in a game? Usually, I'm only concerned about controlling important squares.
Anyway, maybe a 1400 or 1600 player should learn the Lucena and Philidor draw, but the others aren't that important unless it is just giving them a task to hone their thinking skills.

user2253: The more I look at Silman's Complete Endgame Course, the more I agree with how he has organised it. 

Overkill mates where the stronger side is up by at least two rooks worth of material. KQQk, KQRk and KRRk. Especially KRRk is good because it emphasises the importance of having a plan. With queen(s) on the board, mindlessly checking might let the student accidentally fall into a mate, but checking over and over again in KRRk is unlikely to produce progress. 
KQk and KRk. The two basic mates. Further hammering in the importance of having a plan. 
KQkb and KQkn.  Easy enough to win, but especially the latter one takes surprisingly many moves against a stubborn defender. 
KPk, opposition and the square of a passed pawn. Nothing much needs to be said. This is obviously required knowledge.  

These four represent what I'd call the bare minimum needed. And the third is really more of a case of "head fake learning". When one is better at chess, one can obviously figure out how to win KQk{b|n} over the board, so from the viewpoint of teaching theory this is at best marginally useful. The student is actually learning about what the pieces can and cannot do which is always going to be useful.
Beyond this, I think the most practically useful are KQkp, Lucena, Philidor (the KRPkr draw, not the KRBkr win) and a small selection of minor piece theoretical draws (wrong-coloured bishop + rook pawn, KNPk with pawn on h7, etc.).  
You want to minimise memorisation while maximising useful knowledge gained for practical play. Not just in the endgame but also the ability to formulate and execute plans (try KRRkr for this) and gaining familiarity with the capabilities of the pieces. 

3270: <p>When I am introducing beginners to the game, I immediately teach them KQvK, KRvK and KPvK. I follow that up with KBBvK at around the 800 level. Are any resources on when one should learn/teach the following techniques: Lucena win, Philidor draw, KBNvK, KQvKR, KRBvKR, KNNvKP? Each of these teaches valuable lessons with applications beyond just the endgame but the last two may not be worth studying seriously until the IM+ level.</p>
 4418: <p>From teaching my kids I would agree with starting with KQvK and KRvK but I found that the ideas behind KPvK were  a bit too tricky for this level. The opposition and getting the king in front of the pawn were a bit too tricky for beginners. I found KRRvK to be very good not just because it is easy but also because it gives an easy introduction to the "hungry hogs", 2 rooks on the 7th rank. So, KRRvK comes at the same time as the other two basic endings.</p>

<p>Before going for KPvK I would introduce games with just 8Pv8P (no kings), first to get a pawn to the 8th wins, then add kings, same rules. Not being funny but I think this ending comes much later, say at 1200. For Philidor and Lucena I would say around about 1500 or 1600</p>
 3118: <p>This type of question has no real answer, because it is just an opinion... but here goes...</p>

<p>I agree with teaching KQK and KRK immediately. I also usually show KRRK to a new player also. I do this because it is an easy way for them to begin visualizing how the pieces move and control squares, ranks or files. It also shows them how to checkmate the opposing king and the objective of the game without the complexity of 32 pieces on the board. I often show them these mates right after they learn the game.</p>

<p>Except for the Lucena win and Philidor draw, all the others are almost academic unless your a very good player. I don't believe I've ever had to play KQkr or KQkn or KBBk or KBNk in a real game before. At what level do you consistently get to an endgame before someone is lost? I think better players learn them for fun at one point, and they may illustrate some good concepts. e.g. KBNk may show that the N+B work best positioned on the same color squares, but really does that help me in a game? Usually, I'm only concerned about controlling important squares.</p>

<p>Anyway, maybe a 1400 or 1600 player should learn the Lucena and Philidor draw, but the others aren't that important unless it is just giving them a task to hone their thinking skills.</p>
 2253: <p>The more I look at <em>Silman's Complete Endgame Course</em>, the more I agree with how he has organised it. </p>

<ol>
<li>Overkill mates where the stronger side is up by at least two rooks worth of material. KQQk, KQRk and KRRk. Especially KRRk is good because it emphasises the importance of having a plan. With queen(s) on the board, mindlessly checking might let the student accidentally fall into a mate, but checking over and over again in KRRk is unlikely to produce progress. </li>
<li>KQk and KRk. The two basic mates. Further hammering in the importance of having a plan. </li>
<li>KQkb and KQkn.  Easy enough to win, but especially the latter one takes surprisingly many moves against a stubborn defender. </li>
<li>KPk, opposition and the square of a passed pawn. Nothing much needs to be said. This is obviously required knowledge.  </li>
</ol>

<p>These four represent what I'd call the bare minimum needed. And the third is really more of a case of "head fake learning". When one is better at chess, one can obviously figure out how to win KQk{b|n} over the board, so from the viewpoint of teaching theory this is at best marginally useful. The student is actually learning about what the pieces can and cannot do which is always going to be useful.</p>

<p>Beyond this, I think the most practically useful are KQkp, Lucena, Philidor (the KRPkr draw, <em>not</em> the KRBkr win) and a small selection of minor piece theoretical draws (wrong-coloured bishop + rook pawn, KNPk with pawn on h7, etc.).  </p>

<p>You want to minimise memorisation while maximising useful knowledge gained for practical play. Not just in the endgame but also the ability to formulate and execute plans (try KRRkr for this) and gaining familiarity with the capabilities of the pieces. </p>
