Don’t ask me where this question came from. I just happened to be watching an ant crawling across the floor and I just started wondering.
Well, they can jump, but since they have the lowest suicide rate of any of the arthropods they usually don’t.
John
This sounds like a Mailbag question. 
Red ants can jump.
Black ants can.
Ditto other kinds of bugs.
But not termites.
'Cause… white ants can’t jump! [sub]They ain’t got game, either…[/sub]
I read that elephants are the only land animals that can’t jump; everything else smaller is at least capable of jumping. I don’t think ants ever do jump though.
According to this page, Bulldog ants can jump about 10 cm. That’s an incredible distance, in my mind.
This nursery song suggests they dive too:
The ants go marching five by five.
Hurrah! Hurrah!
The ants go marching five by five.
Hurrah! Hurrah!
The ants go marching five by five;
The little one stops to jump and dive,
And they all go marching down
into the ground to get out of the rain.
Boom, boom, boom!
(And National Geographic did an article in 1999 on ants, and described an aquatic one that had adapted to pitcher plants, so I guess they DO dive.) 
I don’t claim to have experience with all species of ants, but when I use a flushing agent, carpenter ants and pavement ants don’t jump around. They run. Now, jumping would get them further away from that which is irritating them, but they don’t do it. So carpenter ants and pavement ants, at least, cannot or will not jump.
I know that an elephant is the only animal that can’t jump…but I think this excludes some insects