We report on a search for gravitational waves from coalescing compact binaries using LIGO and Virgo observations between July 7, 2009 and October 20, 2010. We searched for signals from binaries with total mass between 2 and 25 solar masses; this includes binary neutron stars, binary black holes, and binaries consisting of a black hole and neutron star. The detectors were sensitive to systems up to 40 Mpc distant for binary neutron stars, and further for higher mass systems. No gravitational-wave signals were detected. We report upper limits on the rate of compact binary coalescence as a function of total mass, including the results from previous LIGO and Virgo observations. The cumulative 90%-confidence rate upper limits of the binary coalescence of binary neutron star, neutron star- black hole and binary black holes systems are $1.3 \times 10^{-4}$, $3.1 \times 10^{-5}$ and $6.4 \times 10^{-6} \text{ Mpc}^{-3}\text{ yr}^{-1}$, respectively. We also report on results from a blind injection challenge.