Cool Spot
Cheat mode:
Highlight the music selection on the options screen. Then, press Left, Left, Right three times, Left, Right, Left, Right. Extra lives
and shield options will now be available.

alternate version of the cheat mode code: left left left right right right left right left right.  This one doesn't seem to work either.

Dynamite Dux
Bonus Stage:
At the start of the game you will see a bald man with glasses siting down. Jump on his head and jump off again while pressing buttons one and two. This will take you to a bonus stage.
(the "bald man" is obviously the Colonel Sanders statue, but this code seems to be bogus)

The Lucky Dime Caper starring Donald Duck
Infinite Lives:
Kill Donald and when the continue screen appears press Down + Button 1. You should restart that level with infinite lives.

Quartet
Bonus Round:
In level 4, go to the underworld and destroy the snail in the center of the screen on the block. A warp door appears on the left side of the screen to take you to the bonus round.

Rambo: First Blood Part 2
(This game NEEDS a continue code, but neither of these seem to work)

Continue:
Begin game play in two player mode. Hold 1 + 2 and continuously sweep the D-pad in any direction until the continue option appears. Note: This may only be done through level 2.

Continue game play:
Hold 1 + 2 and rapidly tap Left, Right on both controllers after passing level 3.
 

Rampage
(the game pretty much has unlimited continues as-is, so these are most likely totally bogus)

Infinite Lives:
Wiggle the directional pad clockwise and press buttons one and two at the same time

Infinite Continues:
When the game over message appears onscreen, press both buttons and you will start the game at the beginning of the level you
just completed.

Sonic The Hedgehog
(I think these codes are for the Genesis/Megadrive Sonic, and may have been mis-printed as SMS codes)

Level select:
Press Up, Up, Down, Down, Left, Right, Left, Right at the title screen.

Infinite lives:
When Sonic comes out of the hole, press Left, Right, Down, button 1 and Start.  Hold the Start button untill the level begins.

Space harrier
Unlimited Lives:
For unlimited lives, enter eleven X's on the Game Over screen when you're asked to enter your name.

Thunderblade
Invincibility:
Press up down left right and button one to become invincible.

Time Soldiers
Extra Continues:
At the Game over screen push Up, Up, Down, Down, Button 2. You can get 3 extra continues this way.
(there's 3 continues built into the game, so I think this code may be some kind of error, as I've never gotten it to give me extra continues)

Wonderboy in Monster land
Level select:
Press 1, 1, 2, 2, 1 + 2 when the level and stage numbers are displayed.

Level select (Japanese version):
Hold 1 + 2 + D-pad button and power on the Master System console.

Level select (European version):
Press Down + Start at the title screen for a level select feature. Press Up to select a new starting level.

Wonderboy in Monster World
(seems similar enough to the Monster Land code that it's probably a mis-print)
Extra Money:
Plug a controller into port 2 and press button one to bring up the status screen. Each time you do this you add an extra gold
coin to your tally, repeat this as many times as you like.