In Bowser's Castle, there's a part where you go up a staircase-shaped layer of bricks, then go down the other side. At the top of this area is a mushroom block. If you duck and jump to that block, you can squeeze yourself between the block and the "ceiling". Stand up and you'll go right through the solid wall on your right, taking a valuable shortcut through the castle.
Taken with permission from Flying Omelette.