Play as Akuma
Capcom finally took the hint that stupid button combinations to play as hidden characters were not what people wanted, and so to play as Akuma in this game, you just need to highlight either Magneto, Juggernaut, Dhalsim or Bison and press up. Akuma will then appear.
Fight Akuma
You need to play through the arcade mode and win at least two fights with tag super combo finishers. This has to be done before stage 6. At stage 6, you'll face Akuma. He'll be paired up with another character.
Chun-Li's alternative costume
Highlight Chun-Li and hold down the start button. Then press any button to select her, and she'll appear in her Street Fighter Alpha costume. Her moves are exactly the same as usual though.
Attack a knocked out opponent
If you win you can stop your character's win pose by pressing start and, if you want, continue attacking your opponent. To do this in the Saturn version press L+R, and for the Playstation version, press select.
Playstation version cheats
To play as Apocalypse, beat the game on 5 star difficulty or higher without using a continue. He can only be used in the versus mode, and only one player may select him at a time. To select him, highlight Akuma, hold down the select button, and then press R1.
To get the EX Option menu, at the main menu you need to press Circle, Circle, right, Triangle, R1 incredibly quickly. If done correctly a new screen will appear which lets you turn the hyper combo gauges to infinite, and also lets you set the game mode to "ORIGINAL"... if you do this, you can actually have the same tag team mode featured in the arcade version... kind of. This mode only works in the 2 player versus mode, and even then both players have to pick the same fighters in a certain way, eg Ryu & Wolverine VS. Wolverine & Ryu. But it all works!
SEGA Saturn version cheats
If you beat the game on 8 stars difficulty, you will unlock the "combo gage" which, when set to "full", will let you use hyper combos whenever you want (the gauge will always be full). You will also unlock extra turbo speed settings, not only can you make the game go much faster than normal, but you can also make it go slower.
By beating the game on any difficulty, you will unlock the option to select the same character twice.
Finally if you hold down the L or R buttons when highlighting the Audio option, the words (SHARP S.E.) will appear. This makes the sound effects a little better quality wise -why this isn't turned on by default is anyone's guess.