There are two secret Warp Pipes hidden in certain levels that can help you skip whole Worlds.
World 1-2
Climb up the wall just above where you find the Stamp in this level to find a Warp Pipe that sends you to the start of World 2.
World 4-2
After getting through the caves where you find the Checkpoint Flag, your return to the outside world places you next to a Roulette Block. Climb up the wall above it to access another level of the swamp, where you can see the Warp Pipe that sends you to World 5.