Inside out chess:

Same rules as chess, except no en passant and no castling.

I've never really understood the point to chess variants.  Chess has endless possibilities as it is.

Seems kind of boring! I think white has a forced win.

Using standard pieces and initial positioning, each play can swap the functions of two of their own pieces, before their move. This remains in force until explicitly changed.

I'm pretty sure that white can force a win in inside-out chess.

He can certainly make large material gains after 1. Qg5+!

Pawns can move 2 squares anytime

The king moves like a knight and knights move like a king. For instance, a game could begin like this:

Yes, that was what I was thinking.  I didn't look at all the variations yet, but I'm pretty sure white can at least win material.

Leapfrog chess:  A piece (except the king, pawn, or knights) can jump over only one piece.  For example:

 1. Bb5# and white has a descisive advantage

No, 1... Nc6 or 1... c6.

 Bishop can still jump over the knight.

Apparently, pieces can jump over only one piece. I still feel like there is a big forced win lurking, but I haven't been able to find it.

After 1. Bb5+, after black plays 1... c6 or 1... Nc6, white has no more checks.

Well, he still has more checks. 1. Bb5+ Nc6 2. Bxc6+ bxc6 3. Qh5+ g6 4. Qe5+ Be6 5. Qxh8 d6 6. Bh6 (Nf3) is one way the game could begin. Black isn't looking so hot here. He is down a rook already His knight and bishop are both pinned, and his light square bishop is tied to defending his knight. He can unpin them with Kd7, but he will face more checks if he does so. Even if he doesn't move his king, he can't castle queenside because of the open b file, and his queenside rook is stuck defending a7. White is also threatening Bg5 and Bh6 and Ng5. And of course, black has doubled b pawns, and is completely on the defensive.

White meanwhile has the whole board, the initiative, is on the offensive, hasn't committed any pawns, can develop with tempo, and can castle to either side.

I meant safe checks.  Qh5+ is a blunder, because black can just play Rxh5.

EDIT:  After 1. Bb5+, black can also play 1... c6.  Now Bxc6 would lose the exchange.

How about dice chess? The roll a die and get to make as many moves as the number that you rolled. The objective is to take all of your opponent's pieces.