Gravity, and the conservation of momentum - you have to apply a force to stop something from moving, or cause something to change direction. The sun exerts gravity that pulls the planets toward it, but the planets are already moving, so the pulling causes them to circle the sun rather than just fall in.

Rotation is a consequence of the conservation of angular momentum - you have to apply a torque in order to slow down and stop something from spinning. Nothing is applying such a torque on planets, and they were spinning when they formed, so they're still spinning now.

The reason why planets, such as Earth orbit around the sun is because of the pull of the sun's gravity. And the reason why it travels around the sun is due to Earth's velocity which is in the direction perpendicular to the force of the sun's pull. If we didn't have a sun, the Earth would just travel in a straight line. Imagine if superman were to throw a football with all his strength, it would keep going straight across the Earth which circles the Earth and will eventually hit him, that is basically what we are doing to the sun, we are the football and the earth's velocity is superman's strength. And the strength is hard enough so that gravity doesn't pull the football down to the ground. I am not sure, but I think the reason why we rotate is due to the Earth being at some certain angle.