DAN+, Different KnightsThe Knight is a short-range piece that jumps to 8 different squares, and can visit every square of the board.
Unfortunately, almost all of the possible other 8-direction jumpers are notably weaker than the Knight; they are weak because they are either color-bound or awkward.
NEW! A very good plug-in substitute for the Knight is the Fibnif.
Other than the Fibnif, I can only offer wild substitutes for the Knight. You can use these for fun, but not in tournaments.
The WaffleThe Waffle is a combination of Wazir and Alfil. WA plods one square Rookwise or jumps two squares diagonally; for example, from e4 it can jump to e5, f4, e3, d4, g6, g2, c2, or c6.
The Waffle is a sentimental favorite of mine; it's awkward, but almost, almost as strong as a Knight.
HFThe HF jumps 3 squares Rookwise or one square diagonally; from e4 to e7, h4, e1, b4, f5, f3, d3, or d5.
Its strength is good, but developing it from g1 and b1 is difficult, especially if you have standard Rooks on a1 and h1 that need for it to get out of their way.
FDffmWOuch, what a name!
The FDffmW jumps 2 squares Rookwise or one square diagonally; and in addition, it may move but not capture one square straight forward. From e4, a White FDffmW can move or capture to e6, g4, e2, c4, f5, f3, d3, or d5, or it may move to e5.
This is an example of adding a small power to a piece in order to make it strong enough; as such, it is ugly but instructive.
The FDffmW is color-bound except for its non-capturing move; this adds a special interest to the piece.
DAThe DA jumps two squares diagonally or vertically or horizontally; from e4 it can leap to e6, g6, g4, g2, e2, c2, c4, or c6; and it can get to e6 (for example) even if there is something on e5.
The significant thing about this piece is that it can only see 1/4 of the squares on the board; if it starts the game on g1, it can never ever get to h1, h2, or g2.
This limitation makes it clearly weaker than a Knight, but it can be unexpectedly hard to take advantage of this difference: suppose White has DA's and Black has Knights; as long as Black has a Pawn on his own fifth rank, White has a target, and the DAs can probably do as much useful work in the position as a Knight could; but if Black has no Pawns on his fifth rank, he probably has a disadvantage in space, and a bad position!
Furthermore, when the DA occupies e5 or d5, it is very strong there. Because it is weaker than a Knight, to trade it off would mean taking a small loss in material -- but failing to trade it off allows it to stay in a powerful position!
In the game with DA versus Knight, Black has a probable winning advantage if he has played the game before and has learned how to deal with the DA.