Explosive jumping

Grenade/Rocket Jumping
Grenade jumping, or occasionally known as grenade hopping, is a trick where the player throws a Grenade onto the ground and jumps as it goes off, using the force of the grenade to propel them forward. It is usually done with the Plasma Grenade as the sticking nature is easier to work with (be careful however that you do not throw the plasma grenade directly below you, as you will stick yourself). You can get to higher places with this trick. If the player has got the Sputnik Skull, grenade jumping will be twice as effective as usual. Note that skulls only take effect in campaign and grenade jumping will be normal in any type of multiplayer game.

This can also be done by aiming down with a Rocket Launcher, then shoot and jump at the same time or, if you have an Overshield, both a grenade and a rocket.

To do this on Xbox Live you need to be host.

Fusion Core Super-Jump
This is a neat little trick that works best in the multiplayer level Zanzibar. What you need is:

Any kind of gun (except Rocket Launcher and Brute Shot). Those fusion cores that explode when you shoot or hit them. You can also use a grenade if you wish. An Overshield to protect yourself as you jump. And yourself!

First, push one or two of the fusion cores (no more than two, you will die with three without an overshield) and jump on top of one of them. Then jump and about half a second after you tap the jump button, shoot the fusion cores, and you will fly up above everyone! This is useful to get up to high places for sniping, or to kill another sniper. You can also hide some fusion cores around a corner so when the opponent appears you can give them a nasty surprise.

explosive jumping also can be when u meet a carrier form then jump up to the carrier form when carrier explode you may jump high.

Covenant exploding crates
On any level (preferably Metropolis in Halo 2) go to where a Covenant exploding cylindrical crate (Better known as a Methane Tank) would be situated. This works best with two or more tanks. It can also be done with one exploding cylindrical crate but it is more fun with more. Then stand on top of the exploding cylindrical crate(s) and throw a Grenade. If done right, your body should be blown or "leaped" pretty far.

The Plasma, Frag, and Rocket System ("PFR")
This is a cool trick in Halo and is often used for getting into high ledges.

To do this trick you would need a rocket launcher, plasma grenade and a frag grenade and a warthog. You jump onto the end of the warthog gun (not getting on it) and throw/shoot the weapons in order like this; Plasma grenade, Frag Grenade and Rocket launcher. If you do this right you would be going up pretty high.