Aims. We have searched for temporal variations of narrow absorption lines in high resolution quasar spectra. A sample of five distant sources were assembled, for which two spectra are available, either VLT/UVES or Keck/HIRES, which were taken several years apart. Methods. We first investigate under which conditions variations in absorption line profiles can be detected reliably from high resolution spectra and discuss the implications of changes in terms of small-scale structure within the intervening gas or intrinsic origin. The targets selected allow us to investigate the time behaviour of a broad variety of absorption line systems by sampling diverse environments: the vicinity of active nuclei, galaxy halos, molecular-rich galaxy disks associated with damped Lyα systems, as well as neutral gas within our own Galaxy.Results. Intervening absorption lines from Mg ii, Fe ii, or proxy species with lines of lower opacity tracing the same kind of (moderately ionised) gas appear in general to be remarkably stable (1σ upper limits as low as 10% for some components on scales in the range 10-100 au), even for systems at z abs ≈ z e . Marginal variations are observed for Mg ii lines towards PKS 1229−021 at z abs = 0.83032; however, we detect no systems that display any change as large as those reported in low resolution SDSS spectra.The lack of clear variations for low β Mg ii systems does not support the existence of a specific population of absorbers made of sweptup gas towards blazars. In neutral or diffuse molecular media, clear changes are seen for Galactic Na i lines towards PKS 1229−02 (decrease in N by a factor of four for one of the five components over 9.7 yr), corresponding to structure on a scale of about 35 au, in good agreement with known properties of the Galactic interstellar medium. Tentative variations are detected for H 2 J = 3 lines towards FBQS J2340−0053 at z abs = 2.05454 ( 35% change in column density, N, over 0.7 yr in the rest frame), suggesting there is structure at the 10 au-scale for this warm molecular gas. A marginal change is also seen in C i from another velocity component of the same absorption system ( 70% variation in N(C i).