I suspect that due to the random collision of gas clouds, or similar processes involved in the formation of solar systems, the rotation angle of a solar system - and of the star in the middle - is quite random.
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Uranus.
Mercury and Pluto.
The planet Uranus is tilted "on its side" about 98 degrees to the orbital plane. But all planets in our solar system have some tilt to the side, including Earth which tiles about 23 degrees. (Mercury's tilt is very small.)
The tilt of the Earth's axis relative to the plane of its orbit around the Sun is approximately 23.5 degrees. This tilt is responsible for the changing seasons on Earth as different hemispheres receive varying amounts of sunlight throughout the year.
The tilt of the Earth's axis (about 23.5 degrees) causes the ecliptic plane (the path the Sun appears to take through the sky) to be inclined with respect to the celestial equator. This tilt leads to the changing seasons as the Earth orbits the Sun and causes the ecliptic and celestial equator to intersect at two points, known as the equinoxes.