We report the first detection of X-ray emission from the Quintuplet star cluster and compare its X-ray emission to that of the Arches star cluster. Four point sources are significantly detected near the core of the Quintuplet cluster with a total, absorption-corrected luminosity of 1*1033 ergs s-1. Diffuse, thermal emission is also detected near the core of the Quintuplet cluster with an absorption-corrected luminosity of 1*1034 ergs s-1. We analyze the diffuse and point-like emission from the Arches and Quintuplet and discuss the possibility that they are host to cluster wind outflows. We also present the results of our search for X-ray emission from candidate star clusters in the Galactic center (GC) region. We use extinction estimated by near-IR colors and X-ray spectral fits, as well as other IR properties, to determine if the candidate clusters are new, GC star clusters. We find that three of the six candidate clusters found toward the GC are likely foreground clusters, two of the candidate clusters are not detected in the X-ray data, but have near-IR extinctions consistent with a GC location, and one of the candidate clusters has X-ray and near-IR extinctions consistent with being in the GC. The X-ray and IR emission from the candidate clusters is compared to the known, massive, GC star clusters.