I have real coasters in the living room at my place. I’ve made most of them (needlepoint or tooled leather) over the years and they get changed out seasonally. In the studio, I use a 4" ceramic floor tile with felt spots on the bottom. Out on the deck, no coasters are needed. At the Fella’s, we use whatever magazines or junk mail handy.
I’ve certainly used beer mats, but I prefer to collect them and keep them pristine!
I have tried those ceramic thingys that are supposed to absorb moisture/condensation on the drink, but found them ineffective. (But I only bought one, at the Bush’s Baked Bean Factory, and it’s got some kind of painted[?] design on it … doesn’t work.)
I now have two (count 'em) hand-knitted [by me] cotton coasters. They get wet and limp 
I’m going to read the rest of the post & see if there are any recommendations 
I just use whatever paper scraps are lying around (usually junk mail, reusing the same piece until it gets too wrinkled and dirty), and while some people don’t feel the need for a coaster, I’d rather not have water dripping on the table, even if it won’t damage it (except for cereal, I always drink a glass of milk, which is obviously cold, with meals; also good if you are eating a bowl of something cold).