Three knights is quite a bit easier to force mate than bishop and knight. In some cases, two knights vs a pawn can force mate.
Can 3 knights force mate

According to Nalimov Endgame Tablebases
Three knights can force a win even against a single knight.
http://www.youtube.com/watch?v=AFTkU-FrgeU

I don't understand why 3 knights would be included in a basic endings book. The only positions where promoting to a knight are usuall necessary at endgames are 1) to checkmate instantly 2)prevent a stalemate from promoting to queen.
In the first case obviously it is best, but then the topic is null. In the second case however, a rook would even be better and would be unlikely to stalemate.
Even if the rook does stalemate you will generally have the option of playing a waiting move so the king moves somewhere that promoting to a queen doesnt create a stalemate.
The only situation would be in by allowing this waiting move, the king catches to the pawn your going to promote, and you have no way of getting the other pieces to squares to guard it, but im almost sceptical such a situation has ever happned.

I considered the idea of ''feeling'' how pieces work together. But really, it's almost like studying how 2 kings can work to isolate 1 king in a corner of the board, sure you get to know how 2 kings ''feel'' working together, but it has no real practical value.
2 knights and a bishop would make more sense, even though it is still unlikely, it is quite possible and has value.

"Promoting to a queen forks the black knight and black king."
Black would be going south from the looks of it, so it was the b pawn that was promoted. In this case, I don't see any forking of any sort. The white king can freely move. However, the question has already been asked, why not just get a queen? Then you move Qg1, and then mate on the h file or if the king squirms to the 7th rank then black Ke6.
1. Kh5?? is mate in one - Qh1#

In his book Six Hundred Endings, Lajos Portisch quotes a study composed by Andras Adorjan where underpromotion to a knight would be the only way to win.
Lol there you have it. I didnt consider a position where you need to promote to a knight to prevent a fork like that as the other side attempts to draw.
THEE KNIGHTS MATE
Three Knights can force mate, but the attacking King will have to work with them. It should take a maximum of 20 or 22 moves (I think one of these numbers is the maximum Two Bishops should take) - obviously there are some positions where it is impossible; if it's the defender's turn and they can take one of the Knights or the defender is stalemated.
I'd push the defending King to an edge and then a corner by:
1). build a "fence" - open at the ends but the defending King can't reach them
2). start shrinking the fence
3). eventually the defending King will be "caged"
4). at this point (if not sooner) the attacker will need to work out an exact mating sequence that will take away the last two squares from the defending King.
Sorry I can't give an example at the moment, but it's been a while since I've done it.

I don't understand why 3 knights would be included in a basic endings book. The only positions where promoting to a knight are usuall necessary at endgames are 1) to checkmate instantly 2)prevent a stalemate from promoting to queen.
There is still an other situation, you didn't list. I posted a puzzle in this topic where it happens:
http://www.chess.com/forum/view/more-puzzles/white-play-to-win-unusual-cavalry
This is what happens when we put that position in the Shredder Computer (http://www.shredderchess.com/online-chess/online-databases/endgame-database.html)
- See how the computer forces the mate with 3 Knights:
wikipedia says that “Three knights and a king can force checkmate against a lone king within twenty moves”. (http://en.wikipedia.org/wiki/Checkmate#Three_knights)
two knights cant checkmate bro

two knights can force mate if Opponent makes a blunder in moving the king
The definition of forcing mate means that blunders are not counted in the calculation.

I tried to set up some random positions with 3 knights and let the computer analyze them and it seems it takes max 20 moves to set mate
I don`t think so.
It is possible but it cannot be forced. For the opponent to be mated with two Knights he has to cooperate like a "helpmate".
tigerprowl5 wrote:
"Promoting to a queen forks the black knight and black king."
Black would be going south from the looks of it, so it was the b pawn that was promoted. In this case, I don't see any forking of any sort. The white king can freely move. However, the question has already been asked, why not just get a queen? Then you move Qg1, and then mate on the h file or if the king squirms to the 7th rank then black Ke6.
And why not 1...Qb1-h1# after 1. Kh6-h5?