We have investigated the depolarization effects of light scattered by sharp tips used for apertureless near-field optical microscopy. Dielectric and metal coated tips have been investigated and depolarization factors between 5 and 30% have been measured, changing as a function of the incident light polarization and of the tip shape. The experimental results are in good agreement with theoretical calculations performed by the finite element method, giving a near-field depolarization factor close to 10%. The effect of depolarization has been investigated in polarized tip-enhanced Raman spectroscopy (TERS) experiments; the depolarization gives rise to forbidden Raman modes in Si crystals.