We have systematically studied superconducting instabilities in the repulsive Hubbard model for d-wave and p-wave pairing in various 2D and 3D lattices. Using fluctuation exchange approximation, we consider 3D face centered cubic lattice, 3D body centered cubic lattice, 3D simple cubic lattice, 2D square lattice and 2D triangular lattice, where either strong ferro- or antiferromagnetic spin fluctuation is present. We show that (i) d-wave instability mediated by antiferromagnetic spin fluctuations is stronger than p-wave instability mediated by ferromagnetic spin fluctuations both in 2D and 3D, and (ii)d-wave instability in 2D is much stronger than that in 3D. These amount that the "best" situation is the antiferromagnetic-fluctuation mediated in 2D as far as the single-band Hubbard model on ordinary lattices are concerned. ; Comment: 30 figures, to be published in J. Phs. Soc. Jpn