The skill description is silent about that
There are no anatomical pre-requisites for the use of the Jump skill written directly into the description, only requiring a running start and a (land) movement speed, so you can use the skill properly. This may be an answer to your question:
You can use the jump skill, as long as you have land movement speed. It makes no sense to jump while flying or swimming.
So, by RAW, I don't see anything limiting a snake-like character to jump. Of course, like the other answer pointed out, a race can have a inherent jump limitation, but that's too specific to broaden to what you are going for, I believe.
Either that, or the Monster Manual tries to put some sense into elephants jumping:
Monster Manual pg 7:
Natural Tendencies: Some creatures aren't made for certain types of physical activity. Elephants, despite their great Strength scores, are terrible at jumping. Giant crocodiles, despite their high Strength scores, don't climb well. Horses can't walk tightropes. If it seems clear to you that a particular creature simply is not made for a particular physical activity, you can say that the creature takes a -8 penalty on skill checks that defy its natural tendencies. In extreme circumstances (a porpoise attempting a Climb check, for instance) you can rule that the creature fails the check automatically.
Anyway, this gets a little more complicated when you start to consider severed limbs that were previously used to jump:
- Do you have that in your game? How do you deal with that?
- Where does the movement speed comes from, anatomically?
Again, the core RAW is not enough to answer those two questions, and even including supplements, I believe the later one is never answered given the level of granularity for D&D.