Yes, most moons in the Solar System do spin on their own axes. The rotation of moons is a common phenomenon observed in our Solar System.
The reason our Moon doesn't appear to spin on its own axis is because it is tidally locked with Earth. Tidal locking is a gravitational interaction that results in the same side of an astronomical body always facing the object it is orbiting. In the case of our Moon, it takes the same amount of time to complete one rotation on its axis as it does to orbit around the Earth, which is approximately 27.3 days.
Tidal locking is a consequence of gravitational forces between the Moon and the Earth. Over time, the gravitational forces between the two bodies caused the Moon's rotation to slow down until it became locked in this synchronous rotation, with one side always facing Earth.
Tidal locking is a relatively common phenomenon in the Solar System. For example, many of Jupiter's largest moons, such as Io, Europa, Ganymede, and Callisto, are tidally locked with Jupiter. Similarly, Pluto and its moon Charon are tidally locked with each other.
It's important to note that tidal locking does not mean that the Moon is stationary or not rotating at all. It means that the Moon's rotation and orbital periods are synchronized in a way that the same side always faces Earth, creating the illusion of no rotation when observed from our perspective.