Context. Emission lines formed in decretion disks of Be stars often undergo long-term cyclic variations, especially in the violet-to-red (V/R) ratio of their primary components. The underlying structural and dynamical variations of the disks are only partly understood. From observations of the bright Be-shell star ζ Tau, the possibly broadest and longest data set illustrating the prototype of this behaviour was compiled from our own and archival observations. It comprises optical and infrared spectra, broad-band polarimetry, and interferometric observations. Aims. The dense, long-time monitoring permits a better separation of repetitive and ephemeral variations. The broad wavelength coverage includes lines formed under different physical conditions, i.e. different locations in the disk, so that the dynamics can be probed throughout much of the disk. Polarimetry and interferometry constrain the spatial structure. All together, the objective is a better understand the dynamics and life cycle of decretion disks. Methods. Standard methods of data acquisition, reduction, and analysis were applied. Results. From 3 V/R cycles between 1997 and 2008, a mean cycle length in Hα of 1400-1430 days was derived. After each minimum in V/R, the shell absorption weakens and splits into two components, leading to 3 emission peaks. This phase may make the strongest contribution to the variability in cycle length. There is no obvious connection between the V/R cycle and the 133-day orbital period of the not otherwise detected companion. V/R curves of different lines are shifted in phase. Lines formed on average closer to the central star are ahead of the others. The shell absorption lines fall into 2 categories differing in line width, ionization/excitation potential, and variability of the equivalent width. They seem to form in separate regions of the disk, probably crossing the line of sight at different times. The interferometry has resolved the continuum and the line emission in Brγ and HeI 2.06. The phasing of the Brγ emission shows that the photocenter of the line-emitting region lies within the plane of the disk but is offset from the continuum source. The plane of the disk is constant throughout the observed V/R cycles. The observations lay the foundation for the fully self-consistent, one-armed, disk-oscillation model developed in Paper II.