Does our solar system appear to be unique or are there many solar systems similar to ours in the universe?
There are many other.
Our solar system is not the only system in the universe. There are many solar systems just like ours. If you consider the Kepler program more than 1000 potentially habitable planets have been discovered. Clearly these planets have a Sun like star which is keeping them in orbit. Similarly the Gliese program has also discovered a large number of planets.