user86: If a King, Knight, and Bishop are pitted against the opposing King, is it possible to force checkmate? I find it very hard to do, enough so that I'm not sure whether there's a clean method.

user14678: It is possible, but hard.
Memorizing it doesn't help (it rarely occurs over the board). But, if you try to do it own your own, it will help you with learning how to make better use of minor pieces in the end game.
If you can confine the king to a corner of the same colour as the bishop, then it is over (try it!).
The method most people know is composed of two parts: (i) confine his king to some corner, and (ii) force it to a corner of correct colour (colour of your bishop). Part (ii) is is called the W technique in the lore. Part (i) is easy; part (ii) is not. I recommend against memorizing part (ii).
But being able to do part (i) is a must. Practice it if you cannot do it. If you are good at it, in some positions, you will be able to directly confine the opponent king to a 'right' corner - something that memorizing people cannot. Once you can do part (i) easily, may be just see the 'W technique' more to enjoy than to memorize. It is basically repeatedly forcing the king to move one square closer to the right corner (you fix that corner this time). This is done with a knight maneuver basically. You can then try to do it on your own. Whether you can recreate it or not doesn't matter.
(Note: if you are doing it on your own, it may go beyond the allowed 50 moves and lead to a draw. Don't worry about that. Once you can do it on your own, practice that ending with a friend and try to achieve that mate quicker. )

user2001: Yes it is. Check out this video!
http://www.youtube.com/watch?v=r3EqM17jvOc
The general rule is to get the opponent king in the same corner as your bishop. Use the knight and king to control the squares of opposite color to the color your bishop controls. Then, drive the opponent king to one of the two corners with the correct color!

user12533: [Edited] The winning plan is to force the king into either of the corners which have the same colour as your bishop. 
This is done in a few steps. 

Force the king to one side of the board so he is stuck on either the a/h file or 1st/8th rank
Use the W manoeuvre to force the king to the corner of your bishop, then use the motif of knight check on (e.g. Na3+ to hit b1) then mate with your king on b3, knight covering b1 and Bishop mates on the long diagonal (e.g. Bg7#).  

I have put a detailed review of each step of the ending on my website.

user17: Yes, it can be done. The standard position is to force the enemy king into a corner of the same color as the bishop. Then there are four squares (the corner, the diagonal, and two lateral) squares that need to be attacked.
The bishop attacks the corner and diagonal squares, the king guards one of the lateral squares, and the knight the other one.
[FEN "8/5N2/8/5K2/8/5Bk1/8/8 w - - 0 1"]
[White "K + B + N vs K"]
[Black "White to play and win"]
[Result "1-0"]

1. Ne5 Kh3 2. Kf4 Kh4 3. Ng6+ Kh3 4. Bd5 Kh2 5. Kf3 Kg1 6. Ke2 Kh2 
7. Kf2 Kh3 8. Be6+ Kh2 9. Bg4 {A waiting move to transfer a move to Black, so that the knight will arrive at its destination while giving check.} Kh1 10. Nh4 {The knight starts its journey to f1.} Kh2 11. Nf3+ Kh1 12. Nd2 Kh2 
13. Nf1+ {The all-important destination-check.} Kh1 14. Bf3# {Note: White's bishop can be anywhere on the c8-h3 diagonal (except h3) before this move, and anywhere on the long diagonal to give mate.} 1-0 


user12: Yes it is possible to force mate.  There's a phenomenal video explaining the process on chessvideos.tv.
If you want to practice the endgame, you can do so on the same site as well.

user85: Yes, mate can be forced in 33 moves from nearly any position, according to Wikipedia.
See the standard "w" maneuver cited in that article.

86: <p>If a King, Knight, and Bishop are pitted against the opposing King, is it possible to force checkmate? I find it very hard to do, enough so that I'm not sure whether there's a clean method.</p>
 14678: <p>It is possible, but hard.</p>

<p>Memorizing it doesn't help (it rarely occurs over the board). But, if you try to do it own your own, it will help you with <strong>learning how to make better use of minor pieces in the end game</strong>.</p>

<p>If you can confine the king to a corner of the same colour as the bishop, then it is over (try it!).</p>

<p>The method most people know is composed of two parts: (i) confine his king to some corner, and (ii) force it to a corner of correct colour (colour of your bishop). Part (ii) is is called the W technique in the lore. Part (i) is easy; part (ii) is not. I recommend against memorizing part (ii).</p>

<p><strong>But being able to do part (i) is a must</strong>. Practice it if you cannot do it. If you are good at it, in some positions, you will be able to directly confine the opponent king to a 'right' corner - something that memorizing people cannot. Once you can do part (i) easily, may be just see the 'W technique' more to enjoy than to memorize. It is basically repeatedly forcing the king to move one square closer to the right corner (you fix that corner this time). This is done with a knight maneuver basically. You can then try to do it on your own. Whether you can recreate it or not doesn't matter.</p>

<p>(Note: if you are doing it on your own, it may go beyond the allowed 50 moves and lead to a draw. Don't worry about that. Once you can do it on your own, practice that ending with a friend and try to achieve that mate quicker. )</p>
 2001: <p>Yes it is. Check out this video!</p>

<p><a href="http://www.youtube.com/watch?v=r3EqM17jvOc" rel="nofollow">http://www.youtube.com/watch?v=r3EqM17jvOc</a></p>

<p>The general rule is to get the opponent king in the same corner as your bishop. Use the knight and king to control the squares of opposite color to the color your bishop controls. Then, drive the opponent king to one of the two corners with the correct color!</p>
 12533: <p>[Edited] The winning plan is to force the king into either of the corners which have the same colour as your bishop. </p>

<p>This is done in a few steps. </p>

<ol>
<li>Force the king to one side of the board so he is stuck on either the a/h file or 1st/8th rank</li>
<li>Use the W manoeuvre to force the king to the corner of your bishop, then use the motif of knight check on (e.g. Na3+ to hit b1) then mate with your king on b3, knight covering b1 and Bishop mates on the long diagonal (e.g. Bg7#).  </li>
</ol>

<p>I have put a detailed review of each step of the ending on <a href="http://www.thequietmove.com/endings-bn-mate-king/" rel="nofollow noreferrer">my website</a>.</p>
 17: <p>Yes, it can be done. The standard position is to force the enemy king into a corner of the same color as the bishop. Then there are four squares (the corner, the diagonal, and two lateral) squares that need to be attacked.</p>

<p>The bishop attacks the corner and diagonal squares, the king guards one of the lateral squares, and the knight the other one.</p>

<pre><code>[FEN "8/5N2/8/5K2/8/5Bk1/8/8 w - - 0 1"]
[White "K + B + N vs K"]
[Black "White to play and win"]
[Result "1-0"]

1. Ne5 Kh3 2. Kf4 Kh4 3. Ng6+ Kh3 4. Bd5 Kh2 5. Kf3 Kg1 6. Ke2 Kh2 
7. Kf2 Kh3 8. Be6+ Kh2 9. Bg4 {A waiting move to transfer a move to Black, so that the knight will arrive at its destination while giving check.} Kh1 10. Nh4 {The knight starts its journey to f1.} Kh2 11. Nf3+ Kh1 12. Nd2 Kh2 
13. Nf1+ {The all-important destination-check.} Kh1 14. Bf3# {Note: White's bishop can be anywhere on the c8-h3 diagonal (except h3) before this move, and anywhere on the long diagonal to give mate.} 1-0 
</code></pre>
 12: <p>Yes it is possible to force mate.  There's a phenomenal video explaining the process on <a href="http://www.chessvideos.tv/forum/viewtopic.php?t=802" rel="noreferrer">chessvideos.tv</a>.</p>
<p>If you want to practice the endgame, you can do so on the <a href="http://www.chessvideos.tv/endgame-training/bishop-knight-checkmate.php" rel="noreferrer">same site</a> as well.</p>
 85: <p>Yes, mate can be forced in 33 moves from nearly any position, according to <a href="http://en.wikipedia.org/wiki/Bishop_and_knight_checkmate">Wikipedia</a>.</p>

<p>See the standard "w" maneuver cited in that article.</p>
