In the days when mice had little balls (!) a decent mouse mat made a huge difference to the response of the mouse. these days, when most people have optical mice there really isn't much need for a mouse mat unless you are using it on a shiny surface.
Carlton, yes the mice with the bright lights in the bottom are optical mice, they work just fine on pretty much any surface. with the old style mouse they had a ball that you could see when you looked at the bottom and as bedknobs has said these really didn't work well on many surfaces at all, hence the need for a mat.
Tied in, or ones on a cable, can and usually are these days, optical. They do not have a moving rubber trackball like the old one, they have a beam of light which runs your cursor on screen.
The one that are not tied in, and work without a USB cable are wifi or bluetooth mice.
And as was stated earlier, optical mice do not need a mousemat, though some desk surfaces can be too shiny and slippy and fast, and a piece of matt paper or card will be needed.