We report on the extensive multi-wavelength observations of the blazar Markarian 421 (Mrk 421) covering radio to {gamma}-rays, during the 4.5yr period of ARGO-YBJ and Fermi common operation time, from 2008 August to 2013 February. These long-term observations, extending over an energy range of 18 orders of magnitude, provide a unique chance to study the variable emission of Mrk 421. In particular, due to the ARGO-YBJ and Fermi data, the entire energy range from 100MeV to 10TeV is covered without any gap. In the observation period, Mrk 421 showed both low- and high-activity states at all wavebands. The correlations among flux variations in different wavebands were analyzed. The X-ray flux is clearly correlated with the TeV {gamma}-ray flux, while the GeV {gamma}-rays only show a partial correlation with the TeV {gamma}-rays. Radio and UV fluxes seem to be weakly or not correlated with the X-ray and {gamma}-ray fluxes. Seven large flares, including five X-ray flares and two GeV {gamma}-ray flares with variable durations (3-58d), and one X-ray outburst phase were identified and used to investigate the variation of the spectral energy distribution with respect to a relative quiescent phase. During the outburst phase and the seven flaring episodes, the peak energy in X-rays is observed to increase from sub-keV to a few keV. The TeV {gamma}-ray flux increases up to 0.9-7.2 times the flux of the Crab Nebula. The behavior of GeV {gamma}-rays is found to vary depending on the flare, a feature that leads us to classify flares into three groups according to the GeV flux variation. Finally, the one-zone synchrotron self-Compton model was adopted to describe the emission spectra. Two out of three groups can be satisfactorily described using injected electrons with a power-law spectral index around 2.2, as expected from relativistic diffuse shock acceleration, whereas the remaining group requires a harder injected spectrum. The underlying physical mechanisms responsible for different groups may be related to the acceleration process or to the environment properties.