What would happen if two shockwaves collide?
For example two bombs, placed on each side of the Earth, were to be detonated at the same time creating two extremely powerful shockwaves (powerful enough to go around the Earth a couple of times). When these shockwaves hit each other, would they just keep on going, would they collide creating a third shockwave, or what..?

I asked my science teacher this question some time ago, but he didn't know the answer.

The separate shockwaves would mostly pass through each other, unaffected. This is a common property of waves called superposition.

Here's something I've heard of. It kinda fits yer scenario, Digital Hybrid.

Instead of two bombs on each side of the Earth, there is only one, and it is buried about a mile deep. It detonates, making a shock wave through the crust—much like an earthquake—strong enough to make it all the way to the other side of the Earth. Now on this opposite side, the shock wave would be a closing ring, and it would run into itself at the exact opposite latitude/longitude of the detonation.

This is thought to have happened when that meteor killed the dinosaurs. At that time, the exact opposite latitude/longitude of the impact site was in India. Some scientists think that when the shock wave from the impact ran into itself in India, it created extreme volcanic activity. The volcanoes released large quantities of carbon dioxide, creating a climate change via global warming. This climate change combined with the dirt kicked up by the meteor was enough to kill dinosaurs.

Some scientists also think this happened on one of Uranus's moons. I think it's Miranda. On one side there is a huge crater, and on the other the crust is jagged and jarred.

Of course, I dunno if I remember all of this correctly. Does this kind of shock wave really have this kind of effect?

in effect they would pass right through each other if they were equal forces.
they would meet and then not being able to go any further, would take the easiest route: backwards. so they go backwards with the same force the opposite wave had on contact.