We present results obtained from X-ray observations of the anomalous X-ray pulsar (AXP) 4U 0142+61 taken between 2000-2007 using XMM-Newton, Chandra and Swift. In observations taken before 2006, the pulse profile is observed to become more sinusoidal and the pulsed fraction increased with time. These results confirm those derived using the Rossi X-ray Timing Explorer and expand the observed evolution to energies below 2 keV. The XMM-Newton total flux in the 0.5-10 keV band is observed to be nearly constant in observations taken before 2006, while an increase of ~10% is seen afterwards and coincides with the burst activity detected from the source in 2006-2007. After these bursts, the evolution towards more sinusoidal pulse profiles ceased while the pulsed fraction showed a further increase. No evidence for large-scale, long-term changes in the emission as a result of the bursts is seen. The data also suggest a correlation between the flux and hardness of the spectrum, with brighter observations on average having a harder spectrum. As pointed out by other authors, we find that the standard blackbody plus power-law model does not provide the best spectral fit to the emission from 4U 0142+61. We also report on observations taken with the Gemini telescope after two bursts. These observations show source magnitudes consistent with previous measurements. Our results demonstrate the wide range of X-ray variability characteristics seen in AXPs and we discuss them in light of current emission models for these sources.