Engelbart's original mouse did not require a mousepad; the mouse had two large wheels which could roll on virtually any surface. However, most subsequent mechanical mice starting with the steel roller ball mouse have required a mousepad for optimal performance.
The mousepad, the most common mouse accessory, appears most commonly in conjunction with mechanical mice, because in order to roll smoothly, the ball requires more friction than common desk surfaces usually provide. So-called "hard mousepads" for gamers or optical/laser mice also exist.
Most optical and laser mice do not require a pad. Whether to use a hard or soft mousepad with an optical mouse is largely a matter of personal preference. One exception occurs when the desk surface creates problems for the optical or laser tracking, for example, a transparent or reflective surface.