To progress further in Super Mario, you normally have to defeat Bowser in order to obtain a key to later sections. However this can be subverted by exploiting various glitches.
The attached video is a good example of these tricks. The main methods are using glitches to be able to go through walls, and using the Backwards Long Jump. Another method requires using MIPS the rabbit, however this requires you the have 16 stars, or to use the Backwards Long Jump glitch
The Backwards Long JumpEdit
As it says, this is basically being able to perform the long jump backwards. Doing this on a staircase creates a looping animation, and ends up launching Mario so fast, that he can go through locked doors and skip dialogue boxes. A tutorial to perform this can be found here , or in the above video
The MIPS glitchEdit
The glitch involving MIPS the rabbit allows you to move through the walls is a different manner. Once you catch MIPS, do not collect the star. This way MIPS won't disappear. Walking into the corner of a doorway while holding and pressing Z will sometimes put Mario into the door. Grabbing MIPS from here will allow you to put him on the other side of a door, which you wouldn't normally be able to do. However, doing this near a Star door, will push Mario through the wall and allow him access to areas you shouldn't be able to get to.