Using gamma-ray data collected by the Astro-rivelatore 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 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 1013 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.