Aims: We perform an extensive characterization of the broadband emission of Mrk 421, as well as its temporal evolution, during the non-flaring (low) state. The high brightness and nearby location (z = 0.031) of Mrk 421 make it an excellent laboratory to study blazar emission. The goal is to learn about the physical processes responsible for the typical emission of Mrk 421, which might also be extended to other blazars that are located farther away and hence are more difficult to study. Methods: We performed a 4.5-month multi-instrument campaign on Mrk 421 between January 2009 and June 2009, which included VLBA, F-GAMMA, GASP-WEBT, Swift, RXTE, Fermi-LAT, MAGIC, and Whipple, among other instruments and collaborations. This extensive radio to very-high-energy (VHE; E> 100 GeV) γ-ray dataset provides excellent temporal and energy coverage, which allows detailed studies of the evolution of the broadband spectral energy distribution. Results: Mrk421 was found in its typical (non-flaring) activity state, with a VHE flux of about half that of the Crab Nebula, yet the light curves show significant variability at all wavelengths, the highest variability being in the X-rays. We determined the power spectral densities (PSD) at most wavelengths and found that all PSDs can be described by power-laws without a break, and with indices consistent with pink/red-noise behavior. We observed a harder-when-brighter behavior in the X-ray spectra and measured a positive correlation between VHE and X-ray fluxes with zero time lag. Such characteristics have been reported many times during flaring activity, but here they are reported for the first time in the non-flaring state. We also observed an overall anti-correlation between optical/UV and X-rays extending over the duration of the campaign. Conclusions: The harder-when-brighter behavior in the X-ray spectra and the measured positive X-ray/VHE correlation during the 2009 multi-wavelength campaign suggests that the physical processes dominating the emission during non-flaring states have similarities with those occurring during flaring activity. In particular, this observation supports leptonic scenarios as being responsible for the emission of Mrk 421 during non-flaring activity. Such a temporally extended X-ray/VHE correlation is not driven by any single flaring event, and hence is difficult to explain within the standard hadronic scenarios. The highest variability is observed in the X-ray band, which, within the one-zone synchrotron self-Compton scenario, indicates that the electron energy distribution is most variable at the highest energies. Appendix A is available in electronic form at http://www.aanda.orgThe complete data set shown in Fig. 1 is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/576/A126