The occurrence of stellar wind in the central star of a planetary nebula (CSPN) can be revealed by the presence of P Cygni profiles of high-excitation lines overimposed on its stellar continuum. We examined the entire Far-Ultraviolet Spectroscopic Explorer (FUSE) archive and merged all useful spectroscopic observations of CSPNe to produce the highest quality spectra that can be used to assess the frequency of stellar winds. Furthermore, the individual spectra of each CSPN were compared to search for variability in the P Cygni profile. P Cygni profiles of high-excitation lines have been found in 44 CSPNe, with a clear correlation between the ionization potential of the lines and the effective temperature of the star. We introduce a prescription to derive the terminal wind velocity (v∞) from saturated and unsaturated P Cygni profiles and provide new values of v∞ for these stars. Another 23 CSPNe do not show P Cygni profiles, or else their data in the FUSE archive are not conclusive enough to determine the occurrence of P Cygni profiles. Variability in the P Cygni profile of high-excitation, far-UV lines is found for the first time in six CSPNe, namely Hen 2-131, NGC 40, NGC 1535, NGC 2392, Sp 3, and SwSt 1. This increases up to 13 the number of CSPNe with variable P Cygni profiles in the UV, including those previously reported using IUE or FUSE observations. Variability is seen primarily in the unsaturated P v and Si iv lines, but also in saturated C iii and O vi lines. The CSPNe with variable P Cygni profiles have similar stellar properties (relatively low log (g) and Teff) that suggest they are less evolved CSPNe. Some of the CSPNe with variable P Cygni profiles show O vi lines, while their effective temperature is insufficient to produce this ion. We suggest that this ion is produced by Auger ionization from X-rays associated to shocks in their stellar winds, as is the case in massive OB stars of high ionization potential ions that cannot be abundantly produced by photoionizations.