Hyrule Jump

The Hyrule Jump refers to the act of crossing the open space from Temple's upper right ledge to its bottom-most platform. It can be performed in both Melee and Brawl. Every character can perform the Hyrule Jump, though it is considerably difficult for characters with short recoveries in Melee, in particular Falco and Roy. Since Temple is banned in the standard tournament ruleset, the Hyrule Jump is never seen in competitive gameplay. However, in single-player-mode matches, the Hyrule Jump may be useful in disorienting CPU opponents because they must travel a long distance to get to the player's new position. Another term for this is "Temple Crossing".

Reverse Hyrule Jump
The Reverse Hyrule Jump is the act of performing the Hyrule Jump in reverse, or jumping from the bottom-most platform to the right-most ledge. In Melee, Jigglypuff, Luigi, Kirby, and Mewtwo are known to be able to do the Reverse Hyrule Jump. Link, Peach and Young Link are technically able to perform the Reverse Hyrule Jump as well by using their down B bombs to damage themselves to the point where the bomb's knockback can carry them most of the way to the upper ledge.

In Brawl, Sonic, Jigglypuff, Luigi, Wario, Kirby, Pit, Meta Knight, R.O.B., Fox, Pikachu, Charizard, Zero Suit Samus,and Lucas,  are known to be able to do the Reverse Hyrule Jump. Link, Peach, Snake, and Toon Link are technically able to perform the Reverse Hyrule Jump as well by using their self-damaging bombs as Link, Peach and Young Link can in Melee. Lucario can also perform a very difficult version of the jump by wall-clinging near the top with his extremespeed. Another way is to use his wall jump on the platform you're standing on then use your mid-jump followed by an extremespeed at a small upwards angle, but this is one of the hardest reverse jumps to perform.

Peach, Pit, Wario, Jigglypuff, Kirby, Sonic, Meta Knight, Lucas, and Luigi can do the Reverse Hyrule Jump without using their Up-B attacks.

Down Under Jump
The Down Under Jump is another jump that can be attempted on the Temple stage. It is performed by jumping off the left of the bottom-left landmass, underneath the spike protruding from it, coming back up, and grabbing the left edge of the bottom platform. In Brawl, thirty-two characters can perform this jump; Sonic, Charizard, Lucario, Meta Knight, Kirby, R.O.B., Pit, Toon Link, Jigglypuff, Yoshi, Ness, Lucas, Samus, Zero Suit Samus, Captain Falcon, Pikachu, Diddy Kong, Marth, Wolf, Zelda, Sheik, Squirtle, Ice Climbers (although the secondary climber dies), King Dedede, Luigi, Mario, Ike, Mr. Game and Watch and Wario. Additionally, Snake, Link and Peach can perform the Down Under Jump by damaging themselves with their bombs.

The Reverse Down Under Jump is performing this move in the other direction, moving right from the platform to under the spike and grabbing the left edge of the landmass while moving up. Eighteen Brawl characters can perform the Reverse Down Under Jump; Sonic, Lucario, Meta Knight, Kirby, R.O.B., Pit, Luigi, Wario, Samus, Zero Suit Samus, Charizard, Pikachu, Jigglypuff and Toon Link. Additionally, Peach, Snake and Link can perform the jump by damaging themselves with a C4 or Bomb, respectively, at high damage percentages. Also, although it is considerably harder; Olimar can perform this technique.

Western Temple Jump
This (to a far lesser extent) is also a jump that may be considered "difficult" to rookies with heavier characters. The only characters that seemingly have some trouble with this are Ganondorf and to a smaller degree, Roy.

The Reverse Western Temple Jump is performing the regular Western Temple Jump in the other direction. Again, very few characters have trouble with this jump, as only Ganondorf, and to an extremely lesser extent, Roy and Dr. Mario, may become troublesome to rookies trying to perform this jump.

Falco Shell Jump
This is a jump to be performed by a skilled Falco. One must obtain a Green Shell, as the player leaps off the temple, the player must throw the Shell downwards, and immidiatly afterwards, must fastfall and re-catch the Shell, as well as jumping  back up in the air. This technique can only be (still being researched) performed by Falco, one of the fastest fallers in Brawl. This technique can be performed in many, stylish looking ways, and more importantly, can make a full Hyrule jump (With much skill).

Other Jumps
A "Reverse Down Under Western Temple Jump" is a combination of two of the above jumps where you perform the Reverse Down Under Jump, and land on the westernmost platform on the temple. As of yet, the only characters in Brawl that have been proven to be able to do this are Snake, Sonic, Pit, and Metaknight.

A "Western Temple Down Under Jump" (the same jump but forwards) is theoretically possible but has yet to be done.

A "Full Circle Jump" is a jump that goes all the way around the temple. As of yet, only Meta Knight, Wario as Wario-Man, and Snake have been shown to be able to do this without landing.

Trivia

 * A tiny R.O.B. can complete any Hyrule Jump, as spamming his Down Aerial actually causes him to gain height.
 * As well, Wario as Wario-Man can also complete any Hyrule Jump since all of his aerials (except his Dair) make him gain height.
 * A Tiny and light Samus can also do any Hyrule Jump, as her Down Special causes her to gain height and can be repeated indefinitely.