Classic NES Series: Super Mario Bros.

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Fireworks:
Hit the flagpole at the end of a level when the last digit of the timer is 1, 3, or 6.

Skip to World 5-1:
When starting the game, hold A while selecting the mode at main menu.
Information in this section was contributed by Sonic9jct.

Start from last world:
After you get a "Game Over", hold A while selecting a mode at main menu.
Information in this section was contributed by Sonic9jct.

Luigi costume:
Press Select at the world map to turn Mario's clothes green.

Save and continue from last world:
After the "Game Over" screen appears, press L + R to bring up the menu and select "Save High Score". By holding A and pressing Start at the player selection screen, you will be able to continue from the last world you were at, even after turning off the Game Boy Advance.
Information in this section was contributed by Todd Morris.

Glitch: Get trapped in World 2-2:
At the end of World 2-2, you will see a small opening above the pipe. Crouch down and swim up into the opening. If done correctly, you should slide to the end of the blocks and get trapped until time runs out. Note: You need to be Super Mario or Fire Mario in order to do this.
Information in this section was contributed by Josh DeKorte.