Alternate Music
To listen to alternative music tracks on select stages press and hold either one of the two analog trigger buttons (L or R) when picking your stage. The following stages have alternate music tracks available:

Great Bay: Saria's Song

Hyrule Temple: Fire Emblem

Icicle Mountain: Balloon Fight

Big Blue: Mach Rider

Yoshi's Island: Super Mario Bros. 3

Onett: Earthbound (2)

Pokemon Stadium: Pokemon Battle Theme

Mushroom Kingdoms I and II: Dr. Mario

Battlefield: Multi-Man Melee Theme

Final Destination: Alternate SSBM Theme

Call Team Star Fox
Want to surprise your friends with an unexpected move? Fox McCloud has a cool easter egg maneuver that can only be pulled off on the Great Fox and Venom stages. Find yourself a safe spot where you won't immediately be attacked by an opponent, then rapidly press left, right, left, right on the digital pad. If you did it correctly, Fox will kneel down and call up his friends. Falco, Peppy and Slippy will respond (their faces will appear at the bottom of the screen) and either give you useless advice or tell you to get out of the way as they're about to attack your opponent. Not a very useful move, but a cool thing to amaze your friends with nevertheless. Note that you can only perform this maneuver once every battle.
Earn More Coins
Did you know that the amount of coins you receive after a match is directly related to how often you "smash" the stick during battle? If you want to make easy money, enter the Adventure Mode and make your way all the way through the first level. But before you exit, stand on a secure platform and wiggle the control stick right and left "Decathlon" style. You don't even need to complete smash moves -- moving the stick all the way is enough to earn cash. When you exit and finish the stage you will receive a much higher number of coins. You can do this in any mode or on any level, but you get a lower amount of coins in Vs. Mode (unless all players do this trick at the same time).
Fun With Trophies
While going to the Collection screen to view your trophies, hold L and the trophies will be displayed in rows. Hold R and the trophies will be arranged in a circle. Hold Y and the trophies will be arranged in a triangle. If you have Sound Test unlocked, note that the last music you listened to will also play while you view your trophies.
Peach's Quick Float
In Super Smash Bros. Melee, Princess Peach is the ultimate throwback to Super Mario Bros. 2. Everything from plucking radishes from the ground to using her dress to float for long distances. Her dress is without a doubt one of her most useful tools. Knowing that Peach fanatics want to use it liberally, the developers of the game, HAL, have added in a quick float feature. Instead of having to jump full height to activate the float, you can press Down + X/Y at any time to start floating. Hold the button down to continue hovering. Use it while standing, and you can even hover inches above the ground if you like! A graceful girl indeed.
Pick Your Pose
You can select the pose your character strikes when you win a battle. Simply press B, X, or Y when the match ends. Each button corresponds to a specific winning pose.
Random Character Select
Super Smash Bros. Melee has a built-in random character select feature. Simply place your coin in one of the empty spaces on the selection screen (in the corner next to Pichu or on the opposite site). The game will automatically place your token on a random character.
Random Character Tournaments
Want to set up a more interesting tournament with your friends? When you're at the character/name setup screen in Tournament Melee mode, press the L and R buttons at the same time to change your character icon to Ditto (the shapeshifter of Pokemon fame). This will set that player's character selection to random. Note that this will only work in the Winner Out/Loser Out modes -- not the standard Tournament setting.
Start Battle as Sheik
Want to start a battle as Sheik, not as Zelda? Keep on holding down the A button when you pick Zelda on the character select screen. When the battle begins, you will hear the "unlock chime" from Legend of Zelda and you will start out as Sheik.
Super Shield
Sure, you know that hitting L or R brings up a protective shield -- but how about making it last longer? When blocking, hit L or R lightly (not all the way). This will create a much larger Super Shield that shrinks at a much slower rate than the standard shield. The downside is that it's not as strong. If you want a more powerful shield, press L/R all the way.
Unlocking Hidden Characters
Naturally Super Smash Bros. Melee is filled with playable characters. There are 14 selectable as soon as you boot it up, but you'll find another 11 waiting for you to be unlocked for a total cast lineup of 25 characters. There are genuinely new characters as well as clones. Clones usually share the same moves and attacks as one of the main characters with some subtle adjustments. Apparently there are several ways of unlocking characters either via Vs. matches or single-player mode. Once the conditions are met, the secret character will appear and challenge you to a battle. Win the battle, and you get the character. Here's the ways to do it:

Jigglypuff -- Clear Adventure or Classic mode with any character or play Vs. more than 50 times.
Luigi -- Luigi's appearance depends entirely on your level time for the first Adventure mode level. The time stops the moment you jump the "flag" finish line at the end of the Mushroom Kingdom sidescrolling level. Look at your seconds counter and try to time it so that you get a "2" (as in Luigi, the #2 Mario Brother) in your seconds (like 22, 52, 24, etc). If you got it right, you will see Luigi appear over Princess Peach's Castle in Adventure mode during a cut-scene. Complete the Adventure and he will appear after the credits. Or: Play Vs. Mode more than 800 times.
Young Link (Clone of Link) -- Clear Classic or Adventure mode with 10 characters (two of which have to be Link and Zelda/Sheik) or complete 500 Vs. matches.
Dr. Mario (Clone of Mario) -- Clear Classic or Adventure mode with Mario without using continues (Tip: use Very Easy difficulty) or play more than 100 Vs. matches.
Ganondorf (Clone of Captain Falcon) -- Clear Event Match 29 or play more than 600 Vs. matches.
Pichu -- Clear 200 Vs. Matches, clear Event Match 37, or conquer Classic mode with Mewtwo.
Marth -- Use the original 14 characters at least once in Vs. or another regular mode, or play more than 400 Vs. matches.
Roy (Clone of Marth) -- Clear Classic Mode with Marth without using a continue or play more than 900 Vs. matches.
Falco (Clone of Fox) -- Clear 300 Vs. Matches or beat the 100-Man Melee.
Mewtwo -- Rack up 20:00 hours in Combined Vs. Play Time or play 700 Vs. matches.
Mr. Game & Watch -- Clear Target Test, Classic, or Adventure mode with all 24 characters. Or: play more than 1,000 Vs. matches.
Unlocking Hidden Modes
There are several hidden modes of play hidden within the single-player mode as well as the options menu. Event Matches are a huge part of single-player and at first sight it appears there are only 30. However, as you unlock new characters and stages new Event challenges will be revealed.
Event Matches 31-39 -- You'll need to unlock Jigglypuff, Luigi, Dr. Mario, Falcon, and Young link on top of clearing the first 30 Event Matches.
Event Matches 40-50 -- Unlock all hidden characters and stages. As a special treat there is an extra Event Match that allows you to unlock the special Sound Test feature in the options menu.
Event Match 51 -- Clear all previous events. Sound Test -- Unlock every stage and character. For die-hard players, there is also a hidden Score Display option:
Score Display -- Get a total of 5000 KOs and you will unlock this option that lets you see the players' scores during a match (instead of afterwards). Finally there is a secret All-Star mode which sends you fighting all 25 characters in a gauntlet-type setup. You will have access to three heart recovery items, but no more so you'll have to ration your energy properly.
All-Star mode -- Unlock all 25 secret characters.
It should be noted that there are numerous hidden trophies that unlock randomly with your progress, so be sure to keep your Vs. Match count high and complete as much as possible if you're looking for more trophies.
Unlocking Stages
SSB Melee has a lot of stages to select from. While the select screen only indicates you can unlock five there are actually more than that. Note that there is a certain random element to the unlocking of the first four stages. Sometimes, the first stage you unlock isn't Brinstar. If it didn't unlock at 50 matches, it will unlock at 100, 150, or 200.

Planet Zebes: Brinstar Depths (Metroid) -- Play 50 Vs. matches.
Eagleland: Fourside (Earthbound) -- Play 100 Vs. matches.
F-Zero Grand Prix: Big Blue (F-Zero) -- Play 150 Vs. matches.
Kanto Skies: Poké Floats (Pokémon) -- Play 200 Vs. matches.
Mushroom Kingdom II (Super Mario Bros. 2) -- Get Birdo or Pidgit trophy from Super Mario Bros. 2.
Superflat World: Flat Zone (Game & Watch) -- Unlock Mr. Game & Watch and defeat Classic mode with him.
Battlefield -- Defeat All-Star Mode (secret mode) with any character.
Final Destination -- Clear all 51 Event Matches.
Dream Land (Classic N64 Kirby Stage) -- Complete Target Test successfully with all 25 characters.
Yoshi's Island (Classic N64 Yoshi Stage) -- Hit 1,323 feet (or more) in the Homerun Contest with Yoshi.
Kongo Jungle (Classic N64 DK Stage) -- Finish 15-minute Melee with any character (Tip: use Donkey Kong with his down+B ground slap).
Random Stage Switch -- Unlock all secret stages (except for the classic N64 stages and Battlefield and Final Destination) to reveal a random stage switch. As soon as you start your melee from the character select screen the match will start. This means you don't have to waste time loading the stage select menu.
Easy Back From Select
Want to get back to the previous menu from the character select screen, but don't want to waste time going up and clicking on "back?" Here's a little shortcut: simply hold down the B button and the cancel command will be triggered after a second or so.
Easier 15 Minute Melee
To beat 15 minute melee the easy way, try Mewtwo and go to either edge of the arena. Once you get there, do the B attack and just let the fighters run into you, they rarely hit you and they run into the ball charging.
Extend Samus' Grappling Beam
Rotate the D-PAD in a clockwise or counter-clockwise direction very quickly while pressing Z, R, and A. Done correctly, this will lengthen Samus' grappling hook for the duration of the match, but she will no longer automatically grab onto enemies unless you press the A button.
Fight Big Kirby
In adventure mode, if you beat the Kirby Team in less than a minute, you will fight a bigger, fatter, version of Kirby.
Home Run Hit
To get the needed distance in Home Run Hit (for some trophies) you will need to use Yoshi. Get the bat, then use Yoshi's DOWN+B jumping attack (the paddle kick) to increase the tampon/bag's percentage as much as possible. Five (5) full contact paddle kicks will be enough to send the giant tampon/bag flying with a Bat smash attack (TOWARDS+A).