We present the results of the first long-term (2.2 years) spectroscopic monitoring of a gravitationally lensed quasar, namely the Einstein Cross Q2237+0305. We spatially deconvolve deep VLT/FORS1 spectra to accurately separate the spectrum of the lensing galaxy from the spectra of the quasar images. Accurate cross-calibration of the observations at 31 epochs from October 2004 to December 2006 is carried out using foreground stars observed simultaneously with the quasar. The quasar spectra are further decomposed into a continuum component and several broad emission lines. We find prominent microlensing events in the quasar images A and B, while images C and D are almost quiescent on a timescale of a few months. The strongest variations are observed in the continuum, and their amplitude is larger in the blue than in the red, consistent with microlensing of an accretion disk. Variations in the intensity and profile of the broad emission lines are also reported, most prominently in the wings of the CIII] and in the center of the CIV emission lines. During a strong microlensing episode observed in quasar image A, the broad component of the CIII] is more magnified than the narrow component. In addition, the emission lines with higher ionization potentials are more magnified than the lines with lower ionization potentials, consistent with the stratification of the broad line region (BLR) infered from reverberation mapping observations.