House Entrance Doormat

an anti-vibration mat is a mat which performs the function isolating vibration between that which is above the mat and that which is below. Such a mat might typically be used when mounting a heavy machine which vibrates, onto a concrete floor; in the absence the anti-vibration mat, the machine tend to erode the floor through abrasion. Contrawise, some machines, such as the lithography machines used in chip fabs, need to be isolated from vibrations in their locale, and so are mounted on anti-vibration mats.
a slipmat is a circular piece slippery cloth or synthetic material designed to allow disc jockeys to turn or stop vinyl records on record players, or to scratch.
Chat-Mat is a recordable talking doormat that speaks messages when stepped on. Chat-Mat was invented in 1995 by Ralph Baer, the inventor the first commercial video game system.
a bar mat (not beermat) is a rectangular piece rubber or toweling material that is used to protect the counter top and/or soak up spilt drinks in a bar or pub.