Title Screen Stars
Every time you complete level 8-4, you will add a star to your game's title screen. This will show other players the number of times you have beaten the game.
World 9
To access world 9, you must complete all 8 regular worlds without using a warp zone. After completing level 8-4, you will be taken to level 9-1.
Flagpole Extra Life
To earn an extra life at the end of a level, make sure your coin total is a multiple of 11. Touch the flagpole when the last digit of your remaining time is the same as the last digit in your coin total. For example, touching the flagpole when you have 55 coins and 275 seconds left will earn you an extra life.
World 8 Warp
In level 5-2, run to the set of three elevators. Jump on the first elevator and hit the brick immediately to your left. This brick will turn into a vine. Climb this vine to reach an area in the sky. The warp pipe here will take you to world 8.
Lost Levels
Complete level 8-4 to unlock the lost levels in the main menu. Unlike the game's regular levels, the worlds of the lost levels are marked with letters instead of numbers.
World C Warp
In level A-3, use the spring to jump over the flagpole at the end of the level. Keep running forwards until you reach a warp pipe, which will take you to world C.
World D Warp
In World B-4, go to the very last pipe in the level, which is located next to a lava pit. Inside this pipe is an area with a warp pipe that will take you to world D.