  We report STAR measurements of the longitudinal double-spin asymmetry A_LL,
the transverse single-spin asymmetry A_N, and the transverse double-spin
asymmetries A_Sigma and A_TT for inclusive jet production at mid-rapidity in
polarized p+p collisions at a center-of-mass energy of sqrt{s} = 200 GeV. The
data represent integrated luminosities of 7.6 /pb with longitudinal
polarization and 1.8 /pb with transverse polarization, with 50-55% beam
polarization, and were recorded in 2005 and 2006. No evidence is found for the
existence of statistically significant jet A_N, A_Sigma, or A_TT at
mid-rapidity. Recent model calculations indicate the A_N results may provide
new limits on the gluon Sivers distribution in the proton. The asymmetry A_LL
significantly improves the knowledge of gluon polarization in the nucleon.
