Continue from Game Over Code
You are supposed to restart "Super Mario Bros." from the beginning after losing all of your lives, but you can continue from the level you lost your final life on by using a cheat code. This can only be done while the "Game Over" screen is still up. Press and hold down the "A" button when "Game Over" initially appears, then press the "Start" button.
Unlimited Extra Lives
You can get as many extra lives as you like in World 3-1 of "Super Mario Bros." At the very end of the level, there are two Koopas, the turtle enemies, on the stairs right before the flag. Ignore the first Koopa completely. Jump on the second Koopa and keep bouncing on it. After a few bounces, you will start to gain extra lives. Keep in mind that you will lose the game if you have 100 extra lives, as the game treats this as though you had 0 lives. Avoid getting more than 90 extra lives. This will be more than enough to make it through the rest of the game with ease.
Avoid Enemies
Underground and underwater levels can be easily passed through without any risk of death. The player can cheat at these levels by moving through them in locations untouchable by enemies.
In underground levels, Mario can simply walk over the roof of the level. Smash through a brick or jump through a hole already in the roof. There are no enemies on the roof of these levels, making them very easy to walk through in this manner.
Underwater levels are nearly as easy to move through. Bloopers, the fish, are the main enemies in these levels. They cannot touch Mario if he is walking on the bottom of the level. The other enemies that appear in these levels can still touch Mario if he is on the bottom of the level, but these enemies are fairly rare and easily avoided.