New Super Mario Bros./World 3

World 3 is one of the two worlds after World 2 and leading to World 5, likely being the one you clear first since it is easier to unlock. The theme of this world is beaches and water, although not every level is based around it. Particularly notable is the Ghost House, which should be the first one most will encounter on a normal playthrough. There are only one of each Toad House, while any secret paths branch away from the main route more.

World 3-2
On the first erratic-moving mushroom, you might notice a set of pipes while crossing the wide pit. The pipe you want to go down is the green-colored one at the right, which takes you to a secret area with a P-Switch and a Spin Block. The P-Switch creates a ton of silver coins that you can use the Spin Block to collect. After you're done, go down the right pipe to reach the flagpole area. You must hop across some more tilting platforms before you get to the pole.

Going through this exit leads you to World 3-B, a level which continues the athletic challenge and which can act as a major shortcut across the world.

World 3-Ghost
You can access this secret exit once you get to the third P-Switch, which is the one required to make the hidden door appear. While one did appear close by the moment you hit the switch, there is in fact another hidden door that the switch reveals. Once you hit the P-Switch, immediately run up the first set of stairs, then jump over the gap and fall down the stairs to the left. The hidden exit is to the immediate right of the second P-Switch. Outside, wall jump off the left set of blocks to get to the horizontal block platform. Jump from there to the red flagpole.

Going through this well-hidden back door takes you down a path to the World 3 Cannon. The cannon launches you high above sea level to the rocky peaks of World 6. Watch out for the hike in difficulty!