According to a Wikipedia entry, the name "mouse" was derived from the resemblance of the early models of this computer accessory to the well, what else but this common rodent. It was actually invented by a fellow at the Stanford Research Institute named Douglas Engelbart in 1963. Interestingly the poor fellow failed to re-register the patent before it became popular and widely used, so he didn't get any royalties from it.
Before Engelbart, the Royal Canadian Navy had also invented a similar pointing device using a trackball for their DATAR system. An earlier iteration of the mouse as a pointing device was a bulky device which used two-gear wheels that are perpendicular to each other which translate into motion whenever they are rotated. And if you're wondering when the first fully integrated computer mouse was made available in the market, it was sometime in 1981, when the Xerox 8010 Star Information System came out packed with the first commercially produced computer mouse.