The Erdős number is the academic collaboration distance someone has to Paul Erdős. MathSciNet has a tool to calculate the collaboration distance between two mathematicians (where one may or may not be Erdős). Alas, I am not a mathematician, and if I have an Erdős number at all, it's probably quite large. But the concept of collaboration distance is, of course, not limited to mathematics.
Source: Wikimedia Commons, user h2g2bob, cc-by-sa
Are there any online tools to calculate the collaboration distance between two arbitrary scientists, whether in mathematics or not? In principle this should be possible using any large database of scientific publications. It would be fun to know if I have an Erdős number, or what my distance (and the route!) is to famous scientists in my field.