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Context. Searching for extrasolar planets through radial velocitymeasurements relies on the stability of stellar photospheres. Aims. We aim atcharacterizing the statistical properties of magnetic activity cycles, andstudying their impact on spectroscopic measurements such as radial velocities,line bisectors and line shapes. Methods. We use data from the HARPShigh-precision planet-search sample comprising 304 FGK stars followed overabout 7 years. We obtain high-precision Ca II H&K chromospheric activitymeasurements and convert them to R'HK indices using an updated calibrationtaking into account stellar metallicity. We study R'HK variability as afunction of time and search for possible correlations with radial velocitiesand line shape parameters. Results. We classify stars according to themagnitude and timescale of the Ca II H&K variability, and identify activitycycles whenever possible. We find that 39+/-8% of old solar-type stars in thesolar neighborhood do not show any activity cycles (or only very weak ones),while 61+/-8% do have one. Non-cycling stars are almost only found among Gdwarfs and at mean activity levels log R'HK < -4.95. Magnetic cycle amplitudegenerally decreases with decreasing activity level. A significant fraction ofstars exhibit small variations in radial velocities and line shape parametersthat are correlated with activity cycles. The sensitivity of radial velocitiesto magnetic cycles increases towards hotter stars, while late K dwarfs arealmost insensitive. Conclusions. Activity cycles do induce long-period,low-amplitude radial velocity variations, at levels up to ~25 m/s. Caution istherefore mandatory when searching for long-period exoplanets. However, theseeffects can be corrected to high precision by detrending the radial velocitydata using simultaneous measurements of Ca II H&K flux and line shapeparameters. (Abridged)

The HARPS search for southern extra-solar planets. XXXI. Magnetic  activity cycles in solar-type stars: statistics and impact on precise radial  velocities