Play as Luigi in single player mode
At the "select a file" screen, keep pressed L and R buttons and choose one of your saved game files with the A button.
Now you'll play in the game as Luigi instead of Mario!

Unlock World 7
Defeat the boss in the last castle of World 5 as Mini Mario

Unlock World 4
Defeat the boss in the last castle of World 2 as Mini Mario

Unlock Warp Cannon to World 7
Complete Alternate Route in World 4s Ghost House.

Unlock Original Mario Bros theme and fireworks
If you beat a level with a time left of x11, x22, x33, x44 etc you get fireworks and the original mario level completion song will play.

Skip from world 1 to world 5
Go to the tower in world 1 with the blue shell power-up. Get to the first pipe that shoots you up into the air. On your way back down, there is a gold door. Go in it. There will be a bunch of randomly moving platforms. On the right, there is a gap that always stays the same size. Go through here. Next, you will see three blocks. Use the blue shell ability to break them all, then break the last 3 after that. Go through to the right and finish the level. Now you will unlock the world 1 cannon, which will blast you to world 5.

Extra Lives at Flagpoles
As you may know, jumping onto the flagpole at the stage's end will net you some points (up to 8000). In this game, if you somehow manage to jump high enough and land on the very top of the flagpole, you will automatically receive a 1-Up.

Warp from World 2 to World 5
In Secret Level 2-A, there is a secret exit to the level that will get you access to the warp cannon in World 2. Near the end of the level, there is one last spin jump platform you need to use to reach the final star coin. Instead of stopping once you get the last star coin, continue falling to the right and hit the jump button at the same time you land on the red turtle on the final platform. This will give you enough jump height to reach the platform with the pipe up above you in the little alcove. Go through the pipe and exit the level via the red flag.

Skip from World 5 to 8
You must unlock the World 5 Cannon to travel from World 5 to 8. To unlock the cannon enter the World 5 Ghost House. Get a Mushroom from the blocks. Now, keep advancing up the stairs untill you get to a place with 3 brick blocks on the left side of the screen. Stand on top of them and jump, to reveal 3 invisible blocks. Now wall jump on the left side to get on top of them. Stand on the middle raised block and duck. Jump, to reveal a block with vine in it. Climb up the vine and a Boxing Ghost will see you. Once he breaks out, jump off the vine to avoid taking damage from the Ghost. Kill it and climb back up, and enter the door. Kill the two Walking Pumpkins and stand in the middle. The platform will wobble and as long as you stay in the center you should be ok. When it reaches the top, exit and Jump on the flag pole. A path will open to the cannon on the World Map. Enter and use the cannon to get to world 8, the last World.

Mario Bros. reference
Complete a stage with a time having the last three digits as 111, 222, 333, or 444 to hear the classic Mario Bros. stage completion song with fireworks.

Save Anywhere
To save your game anywhere on the map screen, beat the final castle in World 8. When you restart, you will have a star next to your save and you'll get the "Save" option added to your menu in the map screen.

Warp Zone Cannons
In some worlds, there are cannons you can access (usually through taking secret exits). When you enter the cannon area, there will be a large cannon in the area, and a world number written below it. If you want to warp, simply drop into the cannon and off you go! Here is a list of the known warp zones thus far:

World 5 Warp #1:
Take the secret exit from the World 1 Tower.

World 5 Warp #2:
Take the secret exit from Stage 2-A.

World 6 Warp:
Take the secret exit from the World 3 Ghost House.

World 7 Warp:
Take the secret exit from the World 4 Ghost House.

World 8 Warp:
Take the secret exit from the World 5 Ghost House.