Most stars have planets but exactly what proportion of stars have planets is uncertain because not all planets can yet be detected. That said it has been calculated that there is at least one planet on average per star. One in five Sun-like stars are expected to have an "Earth-sized" planet in the habitable zone.

What percent of stars have planets?

Credit: NASA/Ames/JPL-Caltech. Astronomers from the University of California, Berkeley and the IfA have found that 17 percent of all Sun-like stars have planets one to two times the diameter of Earth in close orbits.

Are there stars without planets?

However, the exact answer to your question "do we know of any stars with no planets" has got to be "no", because there remains a possibility that they have planets that we simply haven't been able to detect, because of limitations in our techniques to detect them.