Pokemon Stadium

Beat R1 Mode, and reload the game. In place of the title screen is a new one.

If you win the tournament on hard, you can get all the pokemon (including all pokegods).

Pokémon Stadium Cup requirements:
Pika Cup
Pokémon can only be between level 15-20.

Petit Cup
Level ranges between 25-30. There is a height requirement though. Height 6'8" limit and weight 44 pounds.

Poké Cup
Only can use 3 Pokémon, levels 50-55. The sum of the Pokémon's levels cannot exceed 155.

Prime Cup
Everything is legal. You can have any level, height, weight, or number of Pokémon. However, your opponents' levels are always 100.

Did you ever notice how some of the Pokémon that appear in Pokémon Stadium have different colors? The secret to the color variations lie in the names you give your Pokémon as well as your trainer ID number (assiged to you in Pokemon Blue, Red or Yellow, whenever you start a new game). While there are a few secret names that change only certain Pokemon's colors, there are a few naming tricks that result in different color variations. For example:
Use only lower caps (ie: poliwhirl)
Reverse the syllables (ie: DRILLBEE)
Abridge the names (ie: Pika)

Register all 151 Pokemon in the Hall of Fame.

Immediately after you choose a move and you want to go first instead of the CPU, hold L and press A. Note: This trick only works about 50% of the time, mostly in the Pika Cup.

If you use an attack that you know will kill the opposing Pokémon, but will hit you with the recoil, make sure that your Pokémon has at least 20 HP left. Use the attack and you will not suffer the recoil damage.

To unlock a hidden 6-on-1 battle with Mewtwo, beat the Gym Leader Castle and get trophies in all 10 tournaments in the Stadium Mode. The map screen will now turn to a night scene and a bonus tournament will open up in which you battle against the psychic super-Pokemon, Mewtwo (#150). Once you beat Mewtwo, you unlock a new game mode.

Once you have beaten both the R-1 mode (including Mewtwo) and the R-2 Mode (including Mewtwo), you are given a set of bonus stickers that you can access in the Gallery Mode. When you're on the Gallery main screen, press and hold L and R and move the Cursor to Print. If you keep the buttons pressed, the Print option will now change to Bonus. You will now have access to a set of 16 bonus "wallpaper" stickers from all the different modes that you can print out at "Snap" Stations.

After beating the R2 Mewtwo, go to the Gallery. Scroll down
to ''Print'' and hold L and R. Print will become ''Bonus''.
Press A to view the game backgrounds, which can be printed
off at a Pokemon Snap station.

If you nickname your Pokemon in the Gameboy game and bring it into Stadium, it will have changed color depending on what you nicknamed it!
This has NOTHING to do with shiny Pokemon, because they were not invented when Stadium was released.
Possibilities range from an orange Pikachu to a seagreen Tentacruel.