In number theory, there is (as far as I know) no currently active preprint server, besides arXiv, and there hasn’t been one since quite a few years (there was an algebraic number theory preprint archive which was incorporated into arXiv around 1998, if I remember right). So I was intrigued to hear a colleague mention a very active preprint server for Linear Algebraic Groups and Related Structures, which contains a fair number of works of great interest which are not available on arXiv (some may be on individual web pages, but not all; for instance, among the more recent ones, neither preprint 292 nor 291 is on arXiv, but they are both quite interesting).
As befits the subject, there are of course plenty of papers there on exceptional groups and other exotic structures.