A fairly large proportion of stars are "double stars" -- two suns orbiting each other. With double stars, there is no necessity for planets to form during the accretion stages of formation, and even if they do there are no stable planetary orbits. So "double star" systems have no planets.
I do not see how a star could form from a cloud of dust and gas into a single body, but I am not an expert, or even well read up in this area. I think that if a star does not have a companion star, then it must have had a planetary system at some stage of its evolution. Conservation of angular momentum pretty much guarantees it.
A good example would be Zeta Reticuli - a binary star system which in cosmological terms, is very close. I forget how close now, maybe 38 light years away? I might be way off with that. Anyway, some exobiologists believe there might be life there, including planets. We haven't detected any planets yet, but we may in the future.