This repost from Gamespot.com, will help you cruise past levels of the classic NES version of Super Mario Bros!
Get to world 3-1, and become Super Mario. At the end of the level, by the staircase before the end flag, you will see two turtles coming down the stairs. Jumping over the first one and then jumping on the second one should cause it to hit the star and bounce back. From here, jump on it and keep yourself off the ground for unlimited 1-ups.
Contributed by: Dude Love Fan
Go to World 1-2. At the pipe that leads to the flag, break two blocks so there’s one at the end touching the pipe. Now duck and jump backward toward the brick (don’t break it!). You should go through the wall and pipe into a warp zone. Jump down the first pipe you see and you will be in the Negative World (-1)!
Contributed by: Grant Evans
To warp to Worlds 2, 3,or 4 during World 1-2, go to the end where the 2 platforms are rising, get on the first platform, and use it to jump onto the highest structure in the middle, then jump on the next rising platform, but this time, when it reaches the top, jump onto the TOP of the level. Walk foward and drop down the small jump, and you can now warp to Worlds 2, 3, or 4 by going down the desired tube, and pressing down.
Contributed by: InternalFlame
The Fireworks Secret
This is a pretty commonly known secret. If you touch the flagpole of any level with either 1, 3, or 6 seconds left on the ones place of the timer, you will get that amount of fireworks. For example, if you touch the flagpole with 126 seconds left on the time, you will get six fireworks!
Contributed by: skcin7
Shoot fireballs as small Mario
Go to either 1-4, 2-4,3-4, etc. and get to Bowser. Make sure you are Big Mario and try to jump over Bowser or run under him. Stand near the Axe and Bowser will start to walk towards you. As he gets near you, jump high, and touch Bowser and the Axe at the same time. If you do it correctly, you will hear the sound as if you were to shrink, but you will just flash and stay big. Go to the next stage, and get a Mushroom. (Yes, there will be a Mushroom instead of a Fire Flower.) When you touch the Mushroom, you will shrink. Then get a Fire Flower, and you’ll have Fire Power as small Mario. (Note: after you do the Bowser/Axe trick, enemies that touch you will be able to kill you when you are Big Mario. When they touch you while you are small Mario after getting the Mushroom or Fire Flower, you will turn back into Big Mario.)
Contributed by: Lhunthangion
Level Warp to World 6,7 or 8
To warp to World 6,7 or 8 during World 4-2, go to the place where three blocks are can be seen (where a pipe can also be seen). Jump below the third block where you can reveal a secret block but be careful on jumping below the 1st block because you can’t break it thus going to the secret warp world unless you are a small Mario. Then step on to it and break the 2nd and the 3rd block. After you have done this, go down, then jump again below the second block now (it should have been broken now). The position of the two revealed blocks must be a stair from right to left. Anyway, step on to the 2nd block then braek the 1st block and there you can see the vine going up. Climb until you reach the day light again. Get some coins if you wish and you can now see three pipes like in the secret warp Worlds 2,3 and 4. Go down your desired pipe.
Contributed by: yodi rr
Warp to World 5
Well this secret is so easy. At the very end place of world 4-2 (where you can see the pipe going to the flag) jump on the long pipe and break the brick above it and go through the end and you can see the pipe going to the World 5.
Contributed by: yodi rr
If you just walk along the sea floor, Bloopers will never be able to kill you because they are forced back up just before they hit the floor(or you).
Contributed by: baconlabs
Access 5-1 from 1-2
To access this warp, you must be Super or Fiery Mario. Go to the pipe at the end of the level and jump on top of it. Jump up and break the block over top of the part of the pipe farthest left. Then, position Mario on the edge of the pipe, with one foot hanging off the edge. Duck, then jump backwards as far right as possible. If done just right, Mario will slide through the pipe and the bricks. Walk over to the warp zone area and enter the middle pipe. This pipe will take you to world 5, level 1. The same area can be acessed from a pipe in the same place in 4-2. However, this is meant to be a warp zone to 5-1, whereas the 1-2 warp to 5-1 is a glitch. After completing the jump trick in level 1-2, you can also go down either of the other two pipes, both of which will take you to Minus World -1.
Contributed by: nintendoman666
If you run out of lives and want to continue then at the game over screen press and hold A then press start at 1 player (or 2 player) and you will start at the beginning of the world at which you died!
Contributed by: cheeseyhuman2
After beating the game, if you do not turn off the console, you will return to the title screen. There, you can press the B Button to start as desired in World 1, 2, 3, 4, 5, 6, 7, or 8.
Contributed by: KeyBlade999
Timer Underflow Glitch
This glitch only works in the castle levels where you fight Bowser at the end – for example, World 1-4, 2-4, 3-4, and so on. It is best to defeat Bowser with Fire Mario or Fire Luigi beforehand, as you must wait out most of the timer to execute this glitch. At the end of the castle levels, there is an axe which you must touch to end the level. If you time your jump correctly (a full jump as the timer goes from 002 to 001 often works) and land on the axe while the timer reads “000”, you’ll continue as normal to the usual sequence at the end of the castle. However, your timer bonus (50 points per second remaining) will be calculated as if you had 999 seconds, not zero, left on the clock. This allows for an easy 49,950 point boost! Note that this glitch, if executed on levels using a flagpole, will prevent you from earning the bonus in that level.
Contributed by: KeyBlade999
Extra jump after collecting a power up in mid-air
This only works with mushrooms and fire flowers. Reveal a power up from under any block which contains one. Now jump onto the power up and release the A button. As Mario is transitioning to the next power up, hold down the A button, and Mario will jump in mid-air!
Contributed by: TheUltimateM4