Using gamma-ray data collected by the Astrorivelatore Gamma ad Immagini LEggero (AGILE) satellite over a period of almost one year (from 2007 July to 2008 June), we searched for pulsed signals from 35 potentially interesting radio pulsars, ordered according to $F_{gamma}propto sqrt{dot{E}} d^{-2}$ and for which contemporary or recent radio data were available. AGILE detected three new top-ranking nearby and Vela-like pulsars with good confidence both through timing and spatial analysis. Among the newcomers we find pulsars with very high rotational energy losses, such as the remarkable PSR B1509-58 with a magnetic field in excess of 10^13 Gauss, and PSR J2229+6114 providing a reliable identification for the previously unidentified EGRET source 3EG 2227+6122. Moreover, the powerful millisecond pulsar B1821-24, in the globular cluster M28, is detected during a fraction of the observations. Four other promising gamma-ray pulsar candidates, among which is the notable J2043+2740 with an age in excess of 1 million years, show a possible detection in the timing analysis only and deserve confirmation.