Incendentally, I have several Super Mario bros. glitches to show:
Walk through walls
In 1-4, pass the first firebar thing and stop on the next platform. You'll notice that the ceiling drops down and almost forms a wall. Slowly go to the right until there's about half a block length between the left edge of the screen and that wall. Direct Mario to the left side of the screen, and jump. Mario should hit his head on the ceiling and land on the wall. (If Mario can't fit, you've scrolled too far. If Mario doesn't get stuck, you haven't scrolled far enough.) Now, hold Left and jump rapidly until Mario starts moving backwards through the wall. At this point, you'll be able to walk through to the end of that low ceiling (beware the firebars...). It is possible to repeat this trick anywhere you find similar floor/ceiling/wall combinations.
Small and Fiery
Being either Super or Fiery Mario, get behind Bowser and let him walk towards you. Jump, and try to land on the Axe and Bowser at the same time. You will defeat Bowser and move on as Super Mario. In the next World, the next powerup you'll get is a Mushroom, which will make Mario small. Next item you'll get is a Fire Flower, which will turn you Fiery, but you will remain small. Note: This will not work in 8-4.
Mario Copperfield
If you are Fiery Mario, you can pull off this cool stunt: Before any level begins (during the "WORLD x-x" screen), press and hold A and B. When the level begins, use the arrow keys to move Mario... and he will be "gliding" along the ground on one foot! Just release A and B and Mario will walk normally again. This also works when Mario is coming out of pipes -- just hold A and B as he is emerging from a pipe....
Koopa Troopa factory
This might work in all similar situations, but an easy place to do this is World 1-1. Near the beginning of the level, there will be two Goombas walking down from a high platform, onto another platform with a Question Block in the middle. Scroll the lower platform almost all the way to the left end of the screen. With perfect timing you can run back and knock the left-most block from below as the last Goomba walks over it. For some reason, this turns the Goomba into an upside-down green Koopa shell as he dies! If you knocked the Mushroom out of the Question Block as you ran by the first time, the shell will be red.
Another good place to pull this off is World 6-1, in the area where you can find the warp-only 1-Up Mushroom (see screen shots 3 - 5 above). If you're in the right spot, you can consistently turn Spinys into Koopa shells. Since Spinys survive knocks from below, the Koopa shells will also survive, and turn into live Koopa Troopas on the ground...