We present the analysis of 103 spectra, collected over more than a decade, of the classical T Tauri star DR Tau observed with the Hamilton echelle spectrograph at Lick Observatory. The star exhibits strong emission lines that show substantial variety and variability in their profile shapes. The emission lines show signatures of both outflow and infall, which vary on multiple timescales. The system shows quasi-periodic variations in line intensity and wavelength, but we are unable to recover a unique period that describes all the data. The Balmer and He I line changes are well correlated and appear to result from real variations in the accretion and wind flows, as opposed to apparent variations caused by changes in the veiling continuum flux. The Balmer line profiles are generally strongly peaked in the red (v ~ 100 km s-1) and do not resemble published theoretical magnetospheric accretion profiles. We suggest that the system is seen nearly pole-on. Coupled with a line emissivity that increases strongly near the stellar surface, this can explain the strongly asymmetric Balmer line profiles. The Ca II and He I emission-line components are found to be very symmetric and Gaussian in shape, suggesting production in a turbulent (possibly magnetic) region. An additional sporadic high-velocity outflow component is seen in the Balmer lines and He I. The main characteristic of the lines is their dramatic variability, which indicates a very dynamic interaction between the star and the disk. This is illustrated in several MPEGs animations showing the line profile variations of DR Tau, which are available on CD-ROM and the World Wide Web.