The Hyrule Jump refers to the act of crossing the open space from Temple's upper right ledge to its bottom-most platform. Every character can perform the Hyrule Jump, though it is considerably difficult for characters with short recoveries, 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. Sonic, Jigglypuff, Luigi, Wario, Kirby, Pit, Meta Knight, R.O.B., Fox, Pikachu, Charizard, Zero Suit Samus, Lucas, and Mewtwo are known to be able to do the Reverse Hyrule Jump. Link, Peach, Snake, Toon Link, 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. 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. There is a video of this on Youtube created by an unknown smasher named TwistHelix. Like the Hyrule Jump, this is more of a show-off technique for fun than a true gameplay maneuver, though in single-player-mode matches it may help in disorienting CPU opponents because they must travel a long distance to get back to your new position.
Peach, Pit, Wario, Jigglypuff, Kirby, Sonic, Meta Knight, 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 Super Smash Bros. Brawl, thirty 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, Squirtle, Ice Climbers (although the secondary climber dies), Dedede, Luigi, Mario, Mr. Game and Watch and Wario. Additionally, Snake, Link and Peach can perform the Down Under Jump by damaging themselves with a C4 or Bomb, respectively, at high damage percentages.
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. Sixteen 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.
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, may become troublesome to rookies trying to perform this jump.
Other Jumps
A "Reverse Down Under Western Temple Jump" is a jump named by MVP, where you perform the Reverse Down Under Jump, and land on the westernmost platform on the temple. As of yet, the only character that has been proven to be able to do this is Snake. MVP also says it is just about as fast (and much easier) to do a normal Reverse Down Under Jump, and then do a Reverse Western Temple Jump. Others reccomendend doing so because doing this jump is rather risky and difficult, and if not done perfectly, it is simply taking more time then stopping would.
A "Western Temple Down Under Jump" (the same jump, but just done fowards) could theoreticaly be 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 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.
External Links
All 26 characters perform the Hyrule Jump in Super Smash Bros. Melee
All SSBB characters perform the Hyrule Jump
[1] SSBB perform Hyrule Jumps