Surprisingly no one has mentioned the bugs in Super Mario Bros. I called them "tricks" back then but now I know better. Apart from the warps there are quite a number of bugs:

1. Slide. Mario can look to be sliding on one foot. Get fireball power (mushroom + flower) and then go down any pipe. When you start to get out of the tunnel hold the B, A and a left/right button. You'll see that Mario/Luigi slides, although this stops after about 5 seconds.

2. The half-body-stuck-in-ground bug. This can be most easily achieved in the first level (this is where I practiced it the most). Towards the end, before the mountain which you climb to slide down the flag pole, there are two goombas. Kill one of them. Then as one of the goombas comes towards you, you'll have to run (hold B), and jump up underneath one of the bricks and kill the remaining goomba at the same time. This is hard to do, so you'll have to try it over and over again until it works. If it works you'll see Mario's legs stuck in ground and he'll be moving to the right. If you want, you can press jump and get out now. If you leave it, you'll keep going even under the mountain.

3. The infinite run. Do the half-body-stuck-in-ground 'trick' and just let yourself keep going. Press down. Keep going right past the flag. There is a solid-brick immediately to the right of the door of the mini-castle on the ground. You have to get under this brick, and then just jump to break it. Then run back and jump on the flag as normal. Mario will then just run past the door and keep running forever. You need to reset your Nintendo to play again.

4. The 'climbing' bug. You can exploit this bug whenever there is an overhead double+ layer of bricks. If I recall correctly, I made use of this bug most frequently in World 1 - Level 2. Where there is the extra life in the ceiling there is a big block of bricks in the middle of the screen. The idea of this bug, is that if you have just enough space (about 3/4 of a brick) between the edge of a screen and the block of bricks, you can run up and do a crouching jump, and get stuck in between the edge of the screen and the bricks. Repeatedly press jump to move up. (I used this bug in case I fell off the edge of the bricks and wanted to get the extra life).

5. Half-tilt or no-tilt of the axe in a Bowser/Koopa level. In any of the worlds in the fourth level, when you go up against a Koopa/Bowser you can jump and touch the axe at the end of the bridge just so that the axe tilts a bit or doesn't move at all. You end the level, but I don't think the bridge is drawn. Basically this is easiest to do when you're just normal Mario (no mushroom / flower). Run and jump about 5/8ths of the bridge. It takes time and practice but it can be done.

6. There is also a method of making Mario have fireball power ('flower power') but having a little Mario. If I recall correctly, Mario can fire fireballs, but dies if he gets touched by an enemy. I can't remember how to do this bug (I think its simultaneously touching a fireball and enemy at same time...but I really can't remember at all. I remember I did it a lot in World 3 - Level 1 and World 4 - Level 1)

7. There are also sort of tricks where you can jump on turtles that are coming down the mountains near flags (world 5 / 8). If you time it just right (bloody hard) you can get it so that when you're on the lower step and you jump, on the way up, you push the turtle, and on the way down, you stop it. If you do this a few times, you go through the 100,200,400,800,1000,2000,5000,1UP points, and get yourself a free life.

These bugs are really hard to find (pure luck!) and really hard to do them if you haven't seen them before. My friends and I were mad about the game and just showed each other these 'tricks'. Open source debugging =).

Note:These bugs don't appear to work in Super Mario All Stars.