Lobster Clasps

Most popular because they are easy to use and attractive. Useful for all purposes.
Spring Clasps

Strong clasp with a spring. They are easy to use and the cheapest clasp.
End Tags

Used at the other end of the beaded piece for lobster or spring clasp can fasten to.
Toggle Clasps

Unique and elegant. Can be used as a feature of the jewellery. Loads of designs available. A little bulky, so suits thicker designs.

Hook & Eye Clasps

They come in many shapes and forms. Some can even make a beautiful feature to the beaded piece. Learn how to make your own hook clasp.

Simple, easy to use and attractive.
Magnetic Clasps

Strong magnets which are simple and attractive. Easy to use. Especially nice to use with hematite beads. Useful for light-medium weight designs.
Lanyard Clasp

Usually used when making key chains or mobile phone decorations. They come in many sizes.
Extenders

A piece of chain up to 5 cm long, used to modify length of necklaces or bracelets. Especially useful with chokers and bracelets as it can be adjusted to fit every person.
End Bar

One side is to connect the clasp and the other multi-looped side is for connecting bracelet and necklace strands for a multi-strand design. Available with 2 or more loops.
There are variations of these clasps which can be used for specific designs. I am sure you will come across some different types in your bead hunt.