New Super Mario Bros./World 1

World 1 is the first world of the game, and it is without a doubt the smallest one, with the least amount of levels contained within it. There are 8 levels in total here, one of which is down an optional path and one that can be skipped by taking a secret exit. There are also two red Toad Houses, two Green Toad Houses and one Mega Toad House. The red Toad Houses can be reached by going down alternate paths and exits, but green and Mega Toad Houses can only be accessed by spending Star Coins.

World 1-2
Just like the warp zones in Super Mario Bros., you can bypass the normal exit pipe if you manage to jump on to the ceiling of the level. To accomplish this, you must tilt the second lever platform as far left as possible, then quickly run to the right and jump. You should reach the small space just above the ceiling. Just run right until you get to a slightly larger space with the third Star Coin and an exit pipe. Go through the pipe and jump to the red flagpole on the other side.

This secret exit opens up a nice shortcut that lets you skip the third level, and even has a red Toad House as a bonus!

World 1-Tower
For this exit, you will need the uncommon Blue Shell item, which can't be found in levels. You must get it from one of the flying blocks visible from the overworld, or from a red Toad House. Make your way to the room with the third Star Coin. Among the many shifting stone blocks in this room's border, there is a mysterious Mario-sized space that remains open at the upper-right corner. Jump to that spot and go right to enter a secret area. From where you end up, jump around to make some hidden blocks appear, one that contains a 1-Up. If you aren't Shell Mario, you won't be able to progress any further and must go through the yellow pipe to return to the main stage. If you are, dash until you duck into your shell, letting you break through the blocks beneath the yellow pipe. Keep going to break past the wall of blocks covering the red pipe. Enter it to get yourself deposited outside the tower, where the red flagpole is.

This secret exit opens up a path to the World 1 Cannon, which launches you far into the chilly plains of World 5. You might not want to take that big of a shortcut if you're inexperienced, as the spike in difficulty is quite significant.