STAR collected data in proton-proton collisions at sqrt(s)=200 GeV with transverse and longitudinal beam polarizations during the initial running periods in 2002--2004 at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory. Results on the single transverse spin asymmetries in the production of high energy forward neutral pions and of forward charged hadrons will be presented. Data have been obtained for double longitudinal asymmetries in inclusive jet production in 2003 and 2004. These data provide sensitivity to the polarization of gluons in the proton. In the future, we aim to determine the gluon polarization over a wide kinematic range using coincidences of direct photons and jets. Furthermore, we aim to determine the polarizations of the u, bar(u), d and bar(d) quarks in the proton by measuring single longitudinal spin asymmetries in the production of weak bosons at sqrt(s) = 500$ GeV.