Can we talk?
Are you well, you know, a Tegestist? 
How do you know if you are? 

A tegestist is a person who collects beer mats.
The name is Latin.  Teges means covering mat. However, the coaster came much later.  In fact it was in use long before it was patented in 1892 by Robert Sputh in Dresden.  The mat serves several functions.  All of them correct: none of them wrong.
The mat serves to primarily catch the condensation from the glassware and protect the surface of the table.  When you place a mat on top of your beer glass it indicates that you are not done with the beer. 

Collecting mats is cheaper than purchasing a t-shirt or a glass.  They take up less space.  They do not shrink, stretch, fade, chip, crack or break.  Best of all they do not require washing!!!
I find that the CD/DVD storage pages are a great way to hold and show off my collection.

It is like a photo album of my beer travels.  There is a story behind everyone of them. 
The challenge is to find an inexpensive source for the budget conscious collector. 
One could go to Staples and pick up a pack of 5 sheets with 4 pockets for a total of 20 coasters to display.  If you only intend to go to 20 breweries in your entire life. 

I found an inexpensive source for 400 pockets for less than $25.00 at the Artisan Deco Store for the more serious tegetstist. 
A large D three ring binder make a good home for these pages and the front allows you to be creative in making up a cover for yourself.  Now they can be proudly displayed on your front room coffee table for you to share and for others to enjoy.