OB stars are crucial for our understanding of Galactic structure, star formation, stellar feedback and multiplicity. In this paper we have compiled a census of all OB stars within 1 kpc of the Sun. We performed evolutionary and atmospheric model fits to observed spectral energy distributions (SEDs) compiled from astro-photometric survey data. We have characterized and mapped 24706 O- and B-type stars (Teff>10000K) within 1 kpc of the Sun, whose overdensities correspond to well-studied OB associations and massive star-forming regions such as Sco-Cen, Orion OB1, Vela OB2, Cepheus and Circinus. We have assessed the quality of our catalogue by comparing it with spectroscopic samples and similar catalogues of OB(A) stars, as well as catalogues of OB associations, star-forming regions and young open clusters. Finally, we have also exploited our list of OB stars to estimate their scale height (76+/-1pc), a local star formation rate of 2896^+417^_-1_M_{sun}_/Myr and a local core-collapse supernova rate of ~15-30 per Myr. We extrapolate these rates to the entire Milky Way to derive a Galactic SFR of 0.67^+0.09^_-0.01_M_{sun}_/yr and a core-collapse supernova rate of 0.4-0.5 per century. These are slightly lower than previous estimates, which we attribute to improvements in our census of OB stars and changes to evolutionary models. We calculate a near-Earth core collapse supernova rate of ~2.5 per Gyr that supports the view that nearby supernova explosions could have caused one or more of the recorded mass extinction events on Earth.