Fight as Gouki/Akuma
Highlight Ryu press LP + MP + HP + Start at the character selection screen.
Ex options
Highlight the "Options" selection on the main screen, then hold L and press A.
DIP switch menu
Successfully complete the game with all the characters, using their Super Turbo versions and the Super versions. This requires completing the game thirty two times. Once this accomplished, hold Y and press Start. This allows you to enter a DIP switch menu to tweak the game.
Play as Anita
At the character selection screen, highlight Donavan, then hold L + R and press A.
Play as Lin Lin
At the character selection screen, highlight Lei Lei, then hold L + R and press A.
Alternate Morrigan's form
At the character selection screen, highlight Morrigan, then hold L + R and press A to play as Morrigan in her bat form.