So, we’ve all heard the old “elephants are the only mammals that cannot jump” (even if, according to SD, African ones can). Is this really true? Are they the only ones? (as always, I’m trying to settle a bet)
Well, there are always white guys.
I seriously doubt that the platypus can jump and I’m reasonably certain that the mole cannot jump.
I suppose you could define a whale’s spy-hop as a sort of jump. But my mind staggers at calling anything from, say, a sealion’s behavioural repertoire a ``jump’’.
And given that bats fly, I’m not sure they really bother jumping much, either, unless you want to consider flight a somewhat prolonged jump…
I doubt that a sloth could jump
I’d also like a see a jumping echidna, armadillo, rhinoceros, hippo or three-toed sloth. 
Here’s the staff report link re African elephants: http://www.straightdope.com/mailbag/melepha2.html
Assuming oyu mean ‘never been observed too’ when you say ‘can’t’ then echidna’s can’t jump. Sloths can’t jump.
If by jump you mean an ability to get all body parts off the ground simultaneously then bats can jump. If you mean somethiing different then presumably whales, dolphins and sea lions can’t jump either.
I wouldn’t say that platypuses can’t jump. They are as active as any other small mammal and quite mobile on land.
Trust me. Echidnas can jump. I accidentally scared the crap out of an echidna hiking in the Grampians in Victoria, Australia.
If you define jump as gettig off the groud completely then any animal that can run can also jump. That applies to hippos and rhinos. Not sure the others can run.