Recent work on adversarial examples has demonstrated that most natural inputs can be perturbed to fool even state-of-the-art machine learning systems. But does this happen for humans as well? In this work, we investigate: what fraction of natural instances of speech can be turned into "illusions" which either alter humans' perception or result in different people having significantly different perceptions? We first consider the McGurk effect, the phenomenon by which adding a carefully chosen video clip to the audio channel affects the viewer's perception of what is said (McGurk and MacDonald, 1976). We obtain empirical estimates that a significant fraction of both words and sentences occurring in natural speech have some susceptibility to this effect. We also learn models for predicting McGurk illusionability. Finally we demonstrate that the Yanny or Laurel auditory illusion (Pressnitzer et al., 2018) is not an isolated occurrence by generating several very different new instances. We believe that the surprising density of illusionable natural speech warrants further investigation, from the perspectives of both security and cognitive science. Supplementary videos are available at: https://www.youtube.com/playlist?list=PLaX7t1K-e_fF2iaenoKznCatm0RC37B_k.