We report the detection by the AGILE satellite of a rapid gamma-ray flare from the powerful gamma-ray quasar PKS 1510-089, during a pointing centered on the Galactic Center region from 1 March to 30 March 2008. This source has been continuosly monitored in the radio-to-optical bands by the GLAST-AGILE Support Program (GASP) of the Whole Earth Blazar Telescope (WEBT). Moreover, the gamma-ray flaring episode triggered three ToO observations by the Swift satellite in three consecutive days, starting from 20 March 2008. In the period 1-16 March 2008, AGILE detected gamma-ray emission from PKS 1510-089 at a significance level of 6.2-sigma with an average flux over the entire period of (84 +/- 17) x 10^{-8} photons cm^{-2} s^{-1} for photon energies above 100 MeV. After a predefined satellite re-pointing, between 17 and 21 March 2008, AGILE detected the source at a significance level of 7.3-sigma, with an average flux (E > 100 MeV) of (134 +/- 29) x 10^{-8} photons cm^{-2} s^{-1} and a peak level of (281 +/- 68) x 10^{-8} photons cm^{-2} s^{-1} with daily integration. During the observing period January-April 2008, the source also showed an intense and variable optical activity, with several flaring episodes and a significant increase of the flux was observed at millimetric frequencies. Moreover, in the X-ray band the Swift/XRT observations seem to show an harder-when-brighter behaviour of the source spectrum. The spectral energy distribution of mid-March 2008 is modelled with a homogeneous one-zone synchrotron self Compton emission plus contributions from inverse Compton scattering of external photons from both the accretion disc and the broad line region. Indeed, some features in the optical-UV spectrum seem to indicate the presence of Seyfert-like components, such as the little blue bump and the big blue bump.