99.9999991% of the speed of light is the target speed for the hadron "bunches." (for those who don't know and are impressed by big numbers)

As for applicable scientific advancements; the LHC should expand our understanding of anti-matter which could advance medical imaging technologies. A PET scan uses positrons (anti-electrons) to make a 3-D map of some part of the body that needs to be inspected, so more sophisticated uses for anti-matter could be just as beneficial.