Play as Akuma
This code is horrendous to get working, but at the character select screen highlight each of the following characters in this order for three seconds: Ryu, Guile, T.Hawk, Cammy, Ryu. Then press start followed by all three punch buttons together. Akuma's picture should appear meaning that the code has worked. This playable version of Akuma is a lot weaker than the one you can fight, and only has single air fireballs, but he is still one of the most powerful characters in the game, so much so that he is banned in tournaments.
Akuma (known as Gouki in the Japanese version) is a hidden character you can fight against. To get him to appear, you need to play through the single player mode and just not use any continues. When you reach M.Bison, Akuma will appear and kill him. Akuma will then turn his attention to you instead and you'll be in for the fight of your life. Akuma is extremely powerful and will do everything possible to stop you from hurting him. His fireballs can blast you back, he can teleport, he can throw two fireballs at you whilst jumping, he can perfectly counter attacks made against him with his dragon punch and he will usually always tech out of any throw. If you manage to dizzy him, he will recover almost immediately.
Play as the Super Street Fighter II versions of characters
You can play as a character with their move set from the previous game by entering a code at the character select screen. These are often referred to as "Old" characters, eg Old Ryu, Old Cammy etc. To access the old versions, press the jab button on the character you want, then quickly imput the code and press the jab button again. To access the alternate color, do the same, but press jab punch and short kick together at the end. I have put each character's old code beneath their color select guides in the characters section.
The old versions of characters obviously have no super combos and cannot tech out of throws. Akuma also doesn't have an old version of himself, since he wasn't even in Super Street Fighter II.
View credits sequence
To view the credits sequence, which features several characters fighting each other, beat the game. You may lose rounds, but you cannot use any continues.
View extra credits sequence
To see a different credits sequence, complete the game without using a continue or losing any rounds. You'll get a credits sequence, featuring a new piece of artwork for each character (excluding Akuma).
Akuma's special ending
If you beat the game with Akuma without using any continues, you'll get to see a special credits sequence which shows each of the opponents you have defeated. You can lose rounds.