Tiny Egg Glitch
In Piranha Groove (4-4), get eaten by the piranha plants in the beginning and get shrunk.  If you can make it up to the cloud above, get as many eggs from the egg block as you can while you're still small.  When you grow back to normal size, you will see that your eggs are very tiny!

Egg Block Glitch
Get either the White Shyguy or a black or white Yoshi egg.  Go to an egg block.  When you hit it, it will give you enough for 6 eggs.  However, since you have a White Shyguy or Yoshi egg, the last egg will drop off.  Rather pointless glitch, though.

Make Yoshi Spin Around
Stand still on the ground.  Make the throwing target appear and place it above Yoshi and to the right of Yoshi.  Move the target across Yoshi to the left; Yoshi should turn around once the target crosses over him.  Move the target over Yoshi to the right, and before he turns himself around, move the target back over him to the left.  Stop moving the target while Yoshi is still turning.
 

(3-3)
Go right from Miss Warp #3.  When the road splits, go in the upper vase.  Go right and enter the upper vase at the next junction.  When you come out there should be Poochy and a pipe below you (you cannot reach either, so don't worry about them).  Go right and go into the first red orange pipe.  There is a "?" bubble in the cave area you enter.
 

Bone Dragon Dungeon (2-2)
Go to the left of Miss Warp #4 and you will see two flowers.  Eat the tulip and aim straight up.  When you are almost to the ceiling, turn back into Yoshi and aim to the right (you may wish to slow your fall by floating).  Pop the "?" bubble.

(2-3)
Find the message block that talks about a big egg.  Go to the left and jump on the last floating rock, then jump on the rock above that and pop the "?" bubble to get black Yoshi..

Torrential Maze (2-4)
In the area with the "ghost vines", get on the first vine.  Jump from vine to vine quickly enough and you will come to an edge with a "?" bubble.  Pop the bubble to claim your prize.

(1-2)
Go the second part and find the 4 moving platforms.  Pop the "?" bubble.

(1-3)
Get to the third part and pop the flying "?" bubble.

(1-4)
Get to the top of the tower and get the umbrella.  Float down on the right side of the tower.  Find the cannon with 2 blue blocks underneath.  Destroy them and walk in to find the block holding White Shyguy.

(2-1)
Fall past the "?" bubbles in the second area.  Hit the blue blocks to the right and get to the other side of them.  Get on top of the 3 blocks near them and hit the bottom block.

(2-2)
After the second ball ride, go into the blue tunnel.  Pop the flying "?" bubble.

(2-3)
Look for Poochy.  Sniff in his spot until you find the area to pound the ground and reveal the blue and white platforms.  Climb up them to find a tunnel; look for 3 blocks surrounding a heart, one of them will contain the shyguy.

(2-4)
Look for the sign that points off the screen with the blue box.  Walk off the screen and hit the "?" ball to the right of the pipe you emerge from.  Climb onto the "!" ball and hit the other "?" ball for the shyguy.

(3-1)
Ride the green dragon until you find the red switch.  Hit it and go up into the clouds to find a tunnel.  Go in to find White Shyguy, Miss Warp #3, and some other stuff.

(3-2)
Look for a melon near a tulip.  Go to the far right and eat the tulip.  Stop at the first level and pop the bubble.

(3-3)
From Miss Warp #3, go to the bottom pot.  Enter the pot and hit the first bubble.

(3-4)
Go to the part with goonies.  Step on them to fly over the pit and hit one of the blue blocks for the shyguy.

(5-3)
Sfter you pass the rain you will see a "?" bubble to the right.  Pop it.

Hidden Message
When you eat a heart fruit and become invincible, a letter formed from coins appears.  Put the letters in order by stage and they will spell out, "YOU ARE YOSHI'S GREAT FRIEND".

Hidden Tune
Let the music on the Trial Mode screen play through.  If you wait long enough, you will hear a very strange tune.  The tune is crude and consists mainly of bleeps and blips.  Thanks to Sadiecat for indentifying this tune as from Mario Paint.

Change Yoshi's Color in Practice Mode
Go to Trial Mode and choose any color Yoshi.  Exit, and then choose Practice Mode and you will have the color Yoshi you picked instead of the default green.  This works with every color except black and white.

Unlimited Continues
In Story Mode, when your last Yoshi is being taken away, hit "RESET".  This only works in the US Version.

Different Ending
Get white and/or black Yoshi (see above).  Beat the game with the hidden Yoshis still alive, and you will see them dancing around the Super Happy Tree at the end.  They will also appear on the character select screen for a new game.

Enable Code [NOTE: This Code Must Be Turned On]
DE00040000000

No Sound
801DCB9E0001
 

*=Before one of the hidden Yoshis or a White Shyguy appears on your character select screen, you must beat the level with them.  If you die, they are lost until you restart Story Mode.  They do not appear in Trial Mode.