Q: What would happen if everyone in the world jumped at the same time?

Physicist: Sounds like a party!

It would create a spherical wave that would descend through the Earth, focus at the core, and then expand again hitting the entire surface again, at more or less the same time, a little under 20 minutes later. In some areas of the Earth there’s a chance that someone might feel or hear a gentle bump. But probably not. Also, don’t worry about the core. It’s already suffering from much worse than a bunch of people jumping around.

A more interesting question might be “can you weaponize hopping?”

Good clean fun? Or the most deadly stealth weapon since HAARP?

There is some precedent for shock waves alone doing damage.  Both Mercury and Saturn’s moon Mimas have suffered massive impacts (the Caloris and Herschel impacts respectively) that created shock waves that moved through/around them and focused on the far side, causing geological scale damage (Allegedly.  It’s hard to say for sure what caused the damage).

Depending on how high the people of the world are willing to jump (without injury), we can generate energy on the order of approximately 1-2 kilotons of TNT. For comparison, the Little Boy nuclear bomb detonated over Hiroshima had an estimated yield of around 15 kilotons.

Now say that the entire world decides that Paris has created more than enough high art, and needs to be dealt with.  By carefully timing when everyone jumps off of their kitchen tables, so that the waves thus created by everyone arrive at the Eiffel tower at the same moment, a fair amount of damage could be done (maybe).  Due to fluctuations in density and material throughout the planet waves have a tendency to get scattered.  As a result, the best you can do is a “fuzzy focus”, like trying to burn something with a smoked-glass magnifying lens.  So here’s a guess:

I’d bet that if everyone on the Earth jumped in the right sequence then you could (mostly) focus the waves at some point on the surface and create an earthquake of no more than 5.0 on the Richter scale.

Here’s another example of “phased array” technology, the terribly named: “hypersonic sound“.