First up. Pencil liner. This is definitely the most common type of liner there is.
pros: easy to use; lots of different colors and brands
cons: sometimes it doesn't show up as dark as other types; unless sharpened, not a perfect line
Ah liquid liner. How I love you.
pros: clean, crisp lines; great for winged out or cat eyes
cons: can be messy; need a steady hand
Cream eyeliner: the next best thing since sliced bread.
pros: lasts all day; easy to smudge; can be applied very dark
cons: very difficult to apply; not very portable messy; easy to smudge
Of course, there are other things you can use as eyeliner. Eyeshadow for example. But these are the three basic liners. Each one is great for different look. So don't worry if you have all three on hand. I won't call you a hoarder.
Which type is your favorite?