My favorite variant that I've found is probably Airplane Chess.  Each army gets 2 planes that move around freely like X-ray queens, jumping (flying) over everyone on an expanded 10x10 board and landing only on an empty square.  When they want to capture they land BEHIND any piece they capture, as if they've bombed the target and landed on an airfield beyond it.    Anyway, this new threat totally changes your entire tactics because now you've got to worry not only about protecting your army from traditional chess captures (direct displacement) but you've also got to plug any holes in your position that an airplane might exploit with its non-displacement captures.  And if you let a plane into the middle of your army, it could potentially fork all kinds of things and bust up your entire position like a real bomber would!

This variant tends to play remarkably smoothly and is a lot of fun.

Now we'll add more on to that, to get my crowded board variant, which is drudgery by comparison, but it's like a heavy espresso shot of chess, so I'm liking it so far:

16 Standard Chessmen for starters.  Then mix in......

2 additional pawns because we're going to a 10x10 board.  (they get up to 3 squares on their initial move to the midline).

2 Gothic Pieces (which go by many names but one always has the combined powers of a B + N and the other is R + N.)

2 airplanes.

2 Champions (strong at close range) from Omega chess, (as are the rest that follow)....

2 Wizards  (their wispy 1,3 or 1,1 moves produce interesting attacks)

1 Fool  (mimics the last piece moved; using the fool properly is an artform).

The Results:

Still testing it out.  So far, it's obviously led to a longer buildup stage of the game, with slowly developing armies but still with an urgency to develop correctly or else you start losing the little skirmishes taking place as each side rolls out.  Where this variant excels is in the middle game, when you start to see the payoff of all that buildup in the form of some deeply kinky combat formations that are a thrill to behold and defend against.  It's much more like the solid walls of combatants you'd see on a mideval battlefield.  Sure, there's some headaches that come with this complex and crowded board and I wouldn't want to be on a short timeclock for this variant, but the sheer number of jumper pieces in the fight (10 + the Fool) keeps things from getting too badly clogged up and the battle stays interesting longer because there's so many powerful pieces.  The  game takes on the dynamic of college basketball, meaning that you can mount a miraculous comeback after taking a beating in the first half of the game.  It's no longer a "one mistake and you're done" enterprise.   And sometimes you have no idea who's really ahead in material if you've traded entirely different kinds of pieces for each other.  Plus, it increases the realism to have some clogging problems with the position, right?  Isn't that how the Romans defeated the Celts and their war chariots, by hemming them in all close together so they couldn't operate?   Ah, the joys of outmaneuvering.

The starting lineups for the armies 

are still something I'm experimenting with.  I think I like the Airplane Chess lineup of having a bump in the center with the center pawns pushed up one square so the knights can start in front of the king and queen.  Moving outward along the back rank.... Bishops stand next to royals.  Then the Gothic pieces.  Then the Airplanes go where the knights just vacated from.  As of right now, I'm trying out the idea that the Champions start on the corner squares and when they move that's when the Rooks are dropped into play in the now-available corners.   The Wizards start on their special island squares diagonally behind the corners (beyond the edge of the board), as in Omega.    The Fool drops into play  when a piece moves from the back rank or castles, or it appears as part of a capture--dropping onto the square a capturing piece started its move from!  (with a time limit of the first 20 moves in which to appear).

I guess this variant is for when you're looking to play one big honking game of chess instead of 2 games of standard chess.   In other words, it doesn't last 3 days like Monopoly, but it's a bit more hardcore than 16 on 16.

Airplanes?

Yeah, airplanes.

I guess the pilots would play this during WWII ?  Whatever. 

Call them something else if you don't want to modernize your army.

Vampires, maybe.

There is actually a similar piece commonly mentioned in chess variants called the grasshopper. It captures as your airplane does, but it doesn't have unlimited leaping ability.

True, though grasshopping is a slightly different mechanic:

With grasshoppers, the chessman they hurdle is unharmed and they capture the enemy on the next square where they land, like a "normal" chess capture.  (what they really need in order to move is to hurdle something).

With airplanes, the last chessman they hurdle IS HARMED, and they land on a different square than they captured on---like a checkers capture, and they can often escape like a ninja if the opponent was only protecting the piece itself and not the landing square!   (What they really need in order to move is any open square along a queen's line of sight.) 

I find grasshoppers very restricted in their movement compared to airplanes.  Planes have complete freedom of movement to "set up" their next capture while grasshoppers must hurdle on every move and it's a bear to get them lined up with a good attacking opportunity.   Now what would be totally crazy is if you had both of these guys on the same chessboard!!!  Make your kings into Scorpion Kings (kings + grasshoppers) to give them an escape abilty AND offensive strike powers!  Then put the king on the same attack line with an airplane and the enemy would be completely unable to defend both threats!!!   If they blocked the airplane's landing square then you'd kill the blocking piece with the grasshopper!  (Unless that would put the king in check!)   In the words of John McCain on SNL, "That'd be crazy....crazy exciting!"

You're right. Locusts are the ones that capture the way you're airplanes do.

sounds fun and hard to lean