Largest reported speedup for a parallel computation?
John Gustafson observed and reported speedups in excess of 1024 on early 80's supercomputers; this led him to the concept of scaled speedup (Gustafson-Barsis law), in contrast to the pessimistic Amdahl-Ware law. 

Right now, in the era of multicore parallel supercomputers equipped with hundreds of thousands or millions of cores, performances are more commonly reported in terms of petaflops and efficiency. For instance, the winners of the last Gordon Bell prize at the Supercomputing 2012 conference, established the current world record for an astrophysical N-body simulation of one trillion particles performed on the full K computer, which appears to be number 4 in the June 2013 top 500 list. They reported 4.45 petaflops on 663,552 cores (the K computer was equipped with 82944 8-core processors in November 2012), and an efficiency (the ratio speedup/cores) of 42%. Translated in terms of speedup, that means a speedup of about 278,691.