In fact "most" simple groups have such covers: if and only if there is a long real root. There is a long and rich history of this topic, going back at least to a paper by Jacque Tits from 1967 (as well as some older work which appeared only in Russian). For a uniform (case-free) treatment see <em>Nonlinear covers of real groups</em>, MR2112326. Also see the references in the paper and in the Mathscinet review.