Are there any solar systems that are not part of a galaxy?

Yes but the community is still discovering the terms. It is thought that many "wandering stars" are not bound to any galaxy. However, it is unknown how frequently they occur, what the sizes of the stars and systems are, or the precise causes. It is thought that they are ejected by disturbances like a merger with another galaxy. read more

However, an existing solar system could be ejected from its home galaxy into extragalactic space. When galaxies collide the tidal forces drag long streams of star and gas away from the home galaxy, along with any solar systems. High velocity stars are observed in our galaxy, traveling fast enough to escape from the Milky Way. read more

For many years scientists have studied our own solar system. But until the last few years, we knew of no other solar systems. This may seem surprising, as the Sun is one of about 200 billion stars (or perhaps more) just in the Milky Way galaxy alone. read more