I call myself a rationalist because learning is impossible with maximum entropy priors, so if we can learn about the world through experience, we must start out with informative priors, which means we have some information about the world that is not attributable to experience. However, I suspect that this kind of position would not be recognized as rationalism by many philosophers.

A more traditional rationalist claim is that reason can provide us with novel information about the world. As an example, consider a Platonist who believes that the integers actually have some kind of independent, objective existence, and aren't just the elements of a useful formal system constructed by humans. In that case, someone who proved Fermat's Last Theorem would have discovered a fact about certain objects in the world, but not through sensory experience.