This could be considered a spoiler to some, so check after the jump. Also check out an interesting little cheat at the bottom.

Unlock Virtual Console Trials

Unlockable How to Unlock
Donkey Kong Exceed 10 hours of play time
F-zero Beat SSE having used captain Falcon
Legend of Zelda Ocarina of Time – Use Toon Link over 10 times
Super Mario USA Win in VS mode with Peach over 5 times
Super Mario World Play yoshi’s Island (melee) over 3 times

Unlockable Characters

Unlockable How to Unlock
Captain Falcon Beat Classic in 12 minutes or less then defeat him in the following match or 70 VS matches
Falco Beat 100-man brawl or play 50 VS matches
Ganondorf Clear Classic on Hard with Link or Zelda OR play 200 VS. matches
Jigglypuff Complete Classic Mode with any character other than Ike or Complete Event Match 20 or 350 VS matches
Lucario Defeat in SSE with Meta Knight or Complete 5 Target Tests with any character or 100 VS matches
Luigi Complete Classic Mode on Easy without continues or meet him in SSE or 22 VS matches
Marth Play 10 Brawls OR finish Classic on any difficulty OR get Marth in the SSE
Mr. Game & Watch Beat classic mode with every character or 250 VS matches
Ness Play five matches OR Reflect ten projecticles AND meet Ness in SSE.
R.O.B. (Robot) Play 160 VS. matches
Snake Play 15 matches on Shadow Moses Island or 130 VS matches
Sonic Complete the Subspace Emissary or 300 VS matches
Toon Link Finish the Classic mode as Link or 400 VS matches
Wolf In the stage “Iseki” (Ruins) skip the first door you pass when being lowered in to the pit. Instead enter the second door at the bottom or 450 VS matches

Contributed By: NostalgicX, Mrakainus, andrew214, IVIonith, patriot4829_V2, CreepyAndNice, jakethepit, Sythe3o0, Mr_Funny, DevilMayBlowChunks
Unlockable Modes

Unlockable How to Unlock
All-Star Mode Unlock all the hidden characters
Boss Battle Mode Defeat the Subspace Emissary with any character

Unlockable Music

Unlockable How to Unlock
02 (Zero Two) Boss Theme (Kirby 64) Have a total of 5000 coins collected in vs. coin matches
100-Man Melee 1 Clear 100-Man Brawl under 4 minutes
3D Hot Rally Title Clear Target Level 5 With Anyone
Bob-Omb Battlefield (Super Mario 64) Have a total of 50 hours of vs. gameplay
Dream Chaser Play 10 vs. matches on Port Town
Ending (Metroid) Play 10 vs. matches on Norfair
Excite Truck Complete Target Test Lv.2 under 19 seconds with any character
Fire Field Complete Event #24
Frozen Hillside Play on the Halberd stage 10 times in VS mode
Goruda Play 10 vs. matches on Halberd
Great Temple Complete Event #33 on Difficult
His World Play 10 vs. matches on Green Hill Zone
His World (Instrumental) Play 10 vs. matches on Green Hill Zone
Ice Climbers (Melee) Clear Classic Mode on Easy with any character
Ike’s Theme Find Ike in the Subspace Emissary
King Dedede’s Theme Complete Event #15
Kuru Kuru Land Get a distance of 400m in Home-Run Contest with one character
Legendary Air Rider Machine Complete Event #13
Love Song (commercial version) Get a combined distance of 12500m in Home-Run Contest
Mach Rider (melee version) Defeat 50 alloys in Endless Multi-Man Brawl
Menu 2 Unlock All 35 Characters
Metroid Prime 2: Multi-Play Play 10 vs. matches on Frigate Orpheon
Mountain and Forest Complete Event #18 on Difficult
Peach Castle (Melee) Unlock all Melee stages
Pokémon Center Collect 200 stickers
Powerhungry Fool Play 10 vs. matches on Castle Siege
Road to Tokiwa Complete Event #8
Snake Eater Play 15 vs. matches on Shadow Moses Island
Song of Storms Complete Event #37
Staff Credits Music Clear Classic Mode on Difficult
Star Wolf (Star Fox: Assault) Complete Event #38 on Difficult
Taru Taru Highlands Clear All-Star Mode on Easy
Underwater BGM (Super Mario Bros) Play 10 vs. matches on Mushroomy Kingdom

Contributed By: Mario-Luige, Boo and Bowser, R351D3NT3V1L4, oddevilmonkey
Unlockable Stage Builder Parts

Unlockable How to Unlock
Edit Parts A Play 10 vs. matches on Stage Builder Stages
Edit Parts B Create 5 Stages in Stage Builder
Edit Parts C Create 15 Stages in Stage Builder

Unlockable Stages

Unlockable How to Unlock
75m Brawl as Donkey Kong 20 times
Big Blue (Melee) Brawl as Captain Falcon 10 times
Electroplankton Stage Complete Event #28
Flat Zone 2 Unlock Mr. Game & Watch
Great Sea Unlock Toon Link
Green Greens Fight as Kirby in VS mode 20 times
Green Hill Zone Unlock Sonic
Jungle Japes Play on any Melee stage 10 times in VS Mode
Luigi’s Mansion Use Luigi in brawl 3 times
Mario Bros Beat Challenge #19
Pokémon Stadium Play on Pokémon Stadium 2 10 times in VS Mode
Spear Pillar Clear stage #25 in Event Mode

Unlockable Target Tests

By clearing various difficulties of Classic, you can unlock different levels of Target Test as outlined below. Note that if you unlock a higher difficulty level before an lower one, you will unlock all the ones before it e.g. If you clear Classic mode once on Intense, you will unlock all the target tests.
Unlockable How to Unlock
Level 2 (Medium) Beat Classic Mode twice on Easy or once on Medium
Level 3 (Hard) Beat Classic Mode twice on Medium or once on Hard
Level 4 (Very Hard) Beat Classic Mode twice on Hard or once on Very Hard
Level 5 (Intense) Beat Classic Mode twice on Very Hard or once on Intense

Selecting Zero Suit Samus

To use Zero Suit Samus at the start of a match, select Samus on the character screen and hold the following button before the match starts with the corresponding controller that is being used:

Gamecube/Classic controller: Hold the R button
Wii Remote with Nunchuk: Hold the Z button
Wii Remote: Hold the Minus (-) button

Note that this also works with stages like Mushroomy Kingdom.