We report experiments on the formation of wave packets consisting of coherently excited ground electronic state rotational levels of I-2, using excitation with an intense nonresonant picosecond laser. As measured in a velocity-map-imaging experiment using Coulomb explosion for the determination of the angular distribution of the molecules, these wave packets display alignment of the internuclear axis along the laser polarization axis, both during the laser interaction and at well-defined time delays following the laser interaction, which correspond to rotational revival times of the molecule. The alignment is studied as a function of the intensity and the pulse duration of the pump laser, the rotational temperature of the molecular beam, the polarization geometry of the pump and probe lasers, and the fragment-ion-charge state used to probe the alignment. We observe experimentally that the alignment at revival times is maximal for intermediate pulse durations of a few picoseconds, where the laser-molecule interaction is neither diabatic nor adiabatic. The alignment increases with intensity, but reaches saturation once the intensity is raised sufficiently high. At this point the degree of alignment is limited by the initial rotational temperature of the molecular beam. Our conclusions are corroborated by model calculations, which are presented in detail in the following paper.