exoplanet - Are there any Stars we know don't have planets?

I am beginning to assume that our solar system is not unique and that every star has several planets.

Not quite, but indeed a study published in Nature in 2012 found that, based on our observations so far, roughly 17% of stars host Jupiter-mass planets, 52% host "Cool Neptunes" and 62% host Super-Earths. (Note that these percentages do not add up to 100%, because they are not mutually exclusive possibilities). This was particularly surprising, because half of all visible stars are believe to be in binary systems, which would make planetary systems very unstable, but some binary systems have been found to have planets too.

So indeed it seems the majority of stars have planets, but it's very unlikely that all of them do.

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.