Chupacabra!

A cat, for an Egyptian-themed set. As owners of cats can testify, they can be quite good jumpers...

A snake with ladders

Just kiddingBut how about an Octoplus?

I like the idea of a big fat coiled snake.  I also like the spider and octopus ideas

a gorila

That thread would be much more interesting if people would explain their reasons.

Horses are the only true animals that can jump in these amazing L-shapes regardless of what is in their way. Long live the knights!

A squid or an octopus or any other cephalopod.

I think an elephant would be an apt replacement for the horse. Hannibal would agree, no?

monkey has my vote, a whole different piece in its behavior, some sort of joker

I'll stick with the Knight as it is, a gallant horse, always ready for battle, able to jump over, around, and on top of, enemies.

In a British-themed set, the English side may have Lions, while the Scots will have their Unicorns.

 We're not really famous for our Unicorns. However, Haggis, now there is a slippy little creature if ever there was one.

 Nah because that's a Bishop in Chinese chess.

I'd changed it to a Deer.

"We're not really famous for our Unicorns."

I based the idea on the British Coat of Arms, as well on 

The lion and the unicorn were fighting for the crown
The lion beat the unicorn all around the town.
Some gave them white bread, and some gave them brown;
Some gave them plum cake and drummed them out of town.

...ah, I see. England is often associated with Lions, but sadly the Unicorn on it does not represent any of the other countries, i.e, Scotland, Wales or Northern Ireland. Our famous animals are the Highland Cow and Salmon. I guess Nessie, if we're including mythical beasts :)

rhino

"sadly the Unicorn on it does not represent any of the other countries..."

The Lion and the Unicorn are time-honoured symbols of the United Kingdom. They are properly speaking heraldic supporters, appearing in the full Royal coat of arms of the United Kingdom. The lion stands for England and the unicorn for Scotland. The combination therefore dates back to the 1603 accession of James I of England who was already James VI of Scotland.

From Wikipedia.

Impressive heraldry from KRASNAYA SHAPOSKA'S GRANNY!