Warp Whistles
The easiest way to skip through the game to later levels is to use warp whistles. They are located at level 1-3, world 1 fortress and a level 2 hammer brother.
In level 1-3, crouch on top of the white block at the end of the level for 5 seconds. This enables you to walk behind the goal line, where you'll find a mushroom house and the first whistle.
In the world 1 fortress, use raccoon Mario to fly over the top of the level to find a door. A hidden door that leads to the whistle is at the far right of the ceiling.
And at the world 2 hammer brother, get the hammer to destroy the rock on the upper right corner of the world 2 map. After you engage the hammer brother on the other side, you'll get a treasure chest with a whistle in it.
Infinite 1 Ups
Go to level 1-2 as raccoon Mario and run up the hill and jump over the horizontal pipe at the beginning of the level, then stand still and wait for Goombas to emerge out of the pipe. After two or three of them come out of the pipe, jump onto one while holding A (to fly into the air). Use your tail to help control your fall back down, and hit another Goomba. They will continue to come out of the pipe, and if you continue to bounce on them without hitting the ground, you will start racking up extra lives.
Morph Hammer Brother
This is a complicated puzzle of a cheat, but it enables you to turn a hammer brother on a world map into a treasure ship full of coins. At the end of a stage, make sure you have a score with a 10-digit that ends in a multiple of eleven, stop the timer at the end of the stage on an even number, and have a number of coins that are a multiple of eleven. When you return to the world maps of worlds 1, 3, 5 or 6, the hammer brother will now be a white ship full of coins.