This intrepid intergalactic freight hauler crash-landed on the Mysterious Planet, and now must escape before his life support runs out and he's exposed to the planet's toxic oxygen atmosphere. Luckily for him, during his time on the planet he discovers...
These little guys are the first species of Pikmin you meet, and probably the type you'll use the most. Their "nose" lets them do more damage in fights, and they're able to withstand even the hottest fires.
The Yellow Pikmin are the second type of Pikmin you encounter, and certainly fit the "middle child" bill. Their light weight lets you throw them higher to solve a few puzzles, and they can carry Bomb Rocks to deal massive damage, but once you've got the parts that require their usage you're usually best off sticking with Red and Blue pikmin.
Blue Pikmin are the last variety you add to your ensemble, and while they're not as combat-capable as Reds or Yellows (with bomb rocks), their ability to breathe underwater using their mouth-like gill lets you reach and conquer vastly more areas than you could otherwise.