Though our Sun is, as far as we know, unique for the number and diversity of planets orbiting it, galactically speaking there are many other stars like it. But planetary formation is not as easy as the Sun makes it look. Astronomers study planetary systems using models of the conditions necessary to initiate planetary formation. After a process of elimination, which considers all the conditions necessary to form planets, many stars are disqualified. There are a variety of reasons why planets would not form around a star.
Some stars seem to have the right stuff, though.
Astronomers have confirmed the presence of planets orbiting 17 stars within 200 light-years of the Sun.