(Abridged) We report on new and archival X-ray and near-infrared observations of the anomalous X-ray pulsar 1E 1048.1-5937 performed between 2001-2007 with RXTE, CXO, Swift, HST, and VLT. During its ~2001-2004 active period, 1E 1048.-5937 exhibited two large, long-term X-ray pulsed-flux flares as well as short bursts, and large (>10x) torque changes. Monitoring with RXTE revealed that the source entered a phase of timing stability in 2004; at the same time, a series of four simultaneous observations with CXO and HST in 2006 showed that its X-ray flux and spectrum and near-IR flux, all variable prior to 2005, stabilized. The near-IR flux, when detected by HST (H~22.7 mag) and VLT (K_S~21.0 mag), was considerably fainter than previously measured. Recently, in 2007 March, this newfound quiescence was interrupted by a sudden flux enhancement, X-ray spectral changes and a pulse morphology change, simultaneous with a large spin-up glitch and near-IR enhancement. Our RXTE observations revealed a sudden pulsed flux increase by a factor of ~3 in the 2-10 keV band. In observations with CXO and Swift, we found that the total X-ray flux increased much more than the pulsed flux, reaching a peak value of >7 times the quiescent value (2-10 keV). With these recent data, we find a strong anti-correlation between X-ray flux and pulsed fraction, and a correlation between X-ray spectral hardness and flux. Simultaneously with the radiative and timing changes, we observed a significant X-ray pulse morphology change such that the profile went from nearly sinusoidal to having multiple peaks. We compare these remarkable events with other AXP outbursts and discuss implications in the context of the magnetar model and other models of AXP emission.
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