When awake mice can be very lively - in the wild they may travel several miles in one night as they forage for food. Therefore most mice will appreciate an exercise wheel. Many of the mouse cages available today already have exercise wheels fitted but if the cage you have bought does not then it is also possible to buy free standing wheels which can be placed in a cage or aquarium.
Any wheel provided should have a solid back and a solid running surface. A mouse can slip on a wheel which has a runged running surface and if it gets its foot or tail caught between the rungs as the wheel is turning it can injure itself. Wheels which have open back or front and back with a bar across the diameter can also injure the mouse if the mouse should stick its head out whilst running.
Although most mice enjoy an exercise wheel, not all do and so you shouldn't be worried if your mouse doesn't use it. Some mice on the other hand can become quite addicted to their exercise wheels.