Low-mass extrasolar planets are presently being discovered at an increased pace by radial velocity and transit surveys, which opens a new window on planetary systems. We are conducting a high-precision radial velocity survey with the HARPS spectrograph, which aims at characterizing the population of ice giants and super-Earths around nearby solar-type stars. This will lead to a better understanding of their formation and evolution, and will yield a global picture of planetary systems from gas giants down to telluric planets. Progress has been possible in this field thanks in particular to the sub-m/s radial velocity precision achieved by HARPS. We present here new high-quality measurements from this instrument. We report the discovery of a planetary system comprising at least five Neptune-like planets with minimum masses ranging from 12 to 25M_{earth}_, orbiting the solar-type star HD 10180 at separations between 0.06 and 1.4AU.