We'll briefly look at each binding style and who it is suited for.

Comb Binding

Plastic comb binding machines will punch holes into the edge of your paper, open the comb as you insert the paper, and close it over a row of evenly spaced plastic rings.
The largest plastic combs that you can buy will bind about 450 pages. Plastic combs are the least flexible binding option since they have a plastic spine that spans the combs preventing the book from being folded over itself like a coil will.
Comb binding machine prices will vary depending on the size of documents they can bind (both in number of pages and length of the paper itself) and whether they manually or automatically punch documents for you. Some models also boast the ability to bind more than one style, such as the Akiles ANYBIND, which will punch, comb and double O wire bind.
Plastic combs are less durable than plastic coils because of the rigid structure and material used to make the combs.
Comb binding is popular for smaller and thinner binding applications such as calendars, cookbooks, and similar binding.

Coil Binding

Coil binding machines punch and bind documents with one continuous spiral coil. Old spiral notebooks were bound with metal coil that had sharp edges and bent easily, so PVC coil is replacing metal in many applications. PVC is more durable because it flexes and also doesn't have sharp ends like metal coils.
Prices for spiral binding machines will vary based on the size of documents they can bind (both in number of pages and length of the paper itself) and whether they manually or automatically punch and insert the coil. An automatic coil inserter is much faster than doing it manually, but an operator must still be holding the paper while the machine inserts the coil.
Spiral binding is ideal for law firms, real estate proposals, and anyone else who needs to quickly (relative to comb binding) and durably bind larger documents.

Wire Binding (also called twin loop, double loop, or wire-o binding)

Wire binding uses metal wires (two per hole punch) that are bent together by the binding machine after the paper is punched and put into the wire ring.
You can wire bind in two sizes or pitches 3:1 and 2:1. The larger is 2:1 pitch and will bind document up to about 300 sheets.
Prices for wire binding machines will vary based on the size of documents they can bind (you'll need a machine with disengageable die if you need to punch legal size documents) and whether they manually or automatically punch and insert the coil. Most wire binding machines do one pitch or the other.
Wire binding is professional looking and durable. It's suitable for law offices, real estate agencies, and anyone who needs to bind larger documents.

ProClick

ProClick is a new type of binding exclusive to GBC that can easily be opened to add or remove pages from a document. It's a continuous bind, so the book can be folded around completely and lies flat. However, ProClick machines will not bind a wide variety of lengths and pages of documents. The ProClick binding spines can be closed and removed by hand or with the machines, and the spines are durable.
A ProClick machine would work well for any company that needs to bind smaller documents as they will only bind up to about 125 pages.

Thermal Binding

You are probably aware of thermal binding as the way paperback books are bound. A one piece front and back cover has glue down the spine, which holds the pages in place. The advantage of thermal binding over the types we've discussed already is the clean look; thermal binding doesn't punch the edges, leaving them vulnerable to tearing and fraying.
There are several types of thermal binding that are beyond the scope of this article. You will find thermal binders at a wide variety of prices for use in anything from small business employee or training manual to large printers who produce phone books.
Unibind binding machines are a subcategory of thermal binding that have become popular for creating photo books and other professional-looking hardback books.

Velobinding (also called strip binding)

A Velobind machine punches holes in your documents and then covers the edges with a plastic strip so the punches are not visible. Although the edges of the paper are visible on one side (as opposed to thermal binding, where the bound edges are covered) Velobinding still makes a durable and clean finished product.
You can Velobind both soft and hard covers, and two different types of spines which make Velobinding a good choice for portfolios, reports, proposals, and courtroom presentations. You can Velobind 2" or up to about 500 sheets.

Saddle Stitchers

Saddle stitchers are machines that punch wire staples through the center fold of the papers being bound. Some saddle stitchers will do both the folding and stapling of a book.
Saddle stitchers are usually in the thousands of dollars and are mostly purchased by printers and similar businesses. Saddle stitching is used for catalogs, brochures, newsletters, and magazines.