We present the Chandra Multiwavelength Project (ChaMP) X-ray point source number counts and cosmic X-ray background (CXRB) flux densities in multiple energy bands. From the ChaMP X-ray point source catalog, similar to 5500 sources are selected, covering 9.6 deg super(2) in sky area. To quantitatively characterize the sensitivity and completeness of the ChaMP sample, we perform extensive simulations. We also include the ChaMP+CDFs (Chandra Deep Fields) number counts to cover large flux ranges from 2 x 10 super(-17) to 2.4 x 10 super(-12) (0.5-2 keV) and from 2 x 10 super(-16) to 7.1 x 10 super(-12) (2-8 keV) ergs cm super(-2) s super(-1). The ChaMP and the ChaMP+CDFs differential number counts are well fitted with a broken power law. The best-fit faint and bright power indices are 1.49 plus or minus 0.02 and 2.36 plus or minus 0.05 (0.5-2 keV), and 1.58 plus or minus 0.01 and 2.59 super(+) sub(-) super(0) sub(0) super(.) sub(.) super(0) sub(0) super(6) sub(5) (2-8 keV), respectively. We detect breaks in the differential number counts that appear at different fluxes in different energy bands. Assuming a single power-law model for a source spectrum, we find that the same population(s) of soft X-ray sources causes the break in the differential number counts for all energy bands. We measure the resolved CXRB flux densities from the ChaMP and the ChaMP+CDFs number counts with and without bright target sources. By adding the known unresolved CXRB to the ChaMP+CDF resolved CXRB, we also estimate total CXRB flux densities. The fractions of the resolved CXRB without target sources are 78% plus or minus 1% and 81% plus or minus 2% in the 0.5-2 and 2-8 keV bands, respectively, somewhat lower than but generally consistent with earlier numbers because of their large errors. These fractions increase by plus or minus 1% when target sources are included.