Super Mario Bros. (NES)

When your game is over, hold A and press Start on the title screen. This lets you continue from the beginning of the world that you were defeated in. For example, if you died in World 3-3, you'll continue from 3-1.
Warp to World 2, 3, or 4
In World 1-2, use the elevator platforms to jump onto the ceiling above the end pipe. Behind the wall you'll find a Warp Zone, where you can skip ahead to World 2, 3, or 4.
Warp to World 5
In World 4-2, walk on the ceiling past the end pipe to find the warp to World 5.
Warp to World 6, 7, or 8
This is the second Warp Zone you can reach from World 4-2. After the first elevator lift, there is a pit and three brick blocks above you. Jump around, and you'll find four hidden coin blocks under the three bricks. Use the hidden blocks you just uncovered to hit the first brick, which holds a Vine. The Vine leads to some bonus Coins and the Warp Zone.
Invisible 1-Up Mushrooms
If you collect all the coins in an x-3 world, the next x-1 stage will have an invisible block containing a 1-Up. For example, getting all the coins in World 4-3 will activate the 1-Up in World 5-1. Alternatively, you can trigger the invisible 1-Up in the x-1 stage by warping to it. Even though you can't do any of those things before World 1-1, it has a hidden 1-Up in it anyway. (Note: For the hidden 1-Up in World 2-1, you only need to collect 21 of the 23 coins in World 1-3.)
Multiple 1-Ups: World 3-1
At the end of World 3-1, two Koopa Troopas walk down the staircase leading to the flagpole. Let the first one go by, then move as far to the right as possible on one of the steps. As the second Koopa Troopa comes down, jump straight up to stomp it, then don't hit another button on the controller. If done correctly (a quick, short jump usually works), Mario will kick the shell into the stair and stomp it again as it ricochets, starting a chain reaction. The points will start to rack up, eventually awarding you 1-Ups for the consecutive stomping. If the chain reaction stops, which may happen sometimes, just press A and the cycle will start again. Try not to get more than 128 extra lives in reserve or your game will end next time you lose a life.
Bonus fireworks
If you touch the flagpole when the last digit of the timer is a 1, 3, or 6, fireworks will go off, giving you 500 points each. The number of fireworks you get matches the last digit on the timer.
Stupid squids
In water levels, the Bloobers can't touch you as long as you're walking on the sea floor.
Buzzy Bowser
Killing Bowser in 3-4 with fireballs reveals that he was really a Buzzy Beetle. The interesting part is that Buzzy Beetle's first appearance as an actual enemy is in 4-2, and he can't be killed with fireballs...
Mario and the beanstalk
After you climb a Vine into a secret area, get back on the Vine, climb up to the top and keep holding Up on the Control Pad. This creates a weird effect, like Mario is dancing on the Vine!
The downside to polesitting
If you jump over any flagpole (it's possible in World 3-3 or in any level with the right Game Genie code), you won't find anything special. The level goes on forever, there are no obstacles/enemies, and you have to wait for time to expire to get out of it.