We have analyzed Chandra ACIS observations of 32 nearby spiral and elliptical galaxies and present the results of 1441 X-ray point sources that were detected in these galaxies. The total point-source X-ray (0.3-8.0 keV) luminosity L_XP is well correlated with the B-band, K-band, and FIR+UV luminosities of spiral host galaxies and is well correlated with the B-band and K-band luminosities of elliptical galaxies. This suggests an intimate connection between L_XP and both the old and young stellar populations, for which K and FIR+UV luminosities are reasonable proxies for the galaxy mass M and star formation rate SFR. We derive proportionality constants α = 1.3 × 10²⁹ ergs s^-1 M and β = 0.7 × 10³⁹ ergs s^-1 (M yr^-1)^-1, which can be used to estimate the old and young components from M and SFR, respectively. The cumulative X-ray luminosity functions for the point sources have significantly different slopes. For the spiral and starburst galaxies, γ ≈ 0.6-0.8, and for the elliptical galaxies, γ ≈ 1.4. This implies that the most luminous point sources—those with L_X 10³⁸ ergs s^-1—dominate L_XP for the spiral and starburst galaxies. Most of the point sources have X-ray colors that are consistent with soft-spectrum (photon index Γ ~ 1-2) low-mass X-ray binaries, accretion-powered black hole high-mass X-ray binaries (BH HMXBs), or ultraluminous X-ray sources (ULXs, also known as IXOs). We rule out hard-spectrum neutron star HMXBs (e.g., accretion-powered X-ray pulsars) as contributing much to L_XP. Thus, for spirals, L_XP is dominated by ULXs and BH HMXBs. We find no discernible difference between the X-ray colors of ULXs (L_X ≥ 10³⁹ ergs s^-1) in spiral galaxies and point sources with L_X ≈ 10³⁸-10³⁹ ergs s^-1. We estimate that 20% of all ULXs found in spirals originate from the older (Population II) stellar populations, indicating that many of the ULXs that have been found in spiral galaxies are in fact Population II ULXs, like those in elliptical galaxies. We find that L_XP depends linearly (within uncertainties) on both M and SFR for our sample galaxies (M 10¹¹ M and SFR 10 M yr^-1).