  This paper presents the results from point-like neutrino source searches
using ten years of IceCube data collected between Apr.~6, 2008 and Jul.~10,
2018. We evaluate the significance of an astrophysical signal from a point-like
source looking for an excess of clustered neutrino events with energies
typically above $\sim1\,$TeV among the background of atmospheric muons and
neutrinos. We perform a full-sky scan, a search within a selected source
catalog, a catalog population study, and three stacked Galactic catalog
searches. The most significant point in the Northern hemisphere from scanning
the sky is coincident with the Seyfert II galaxy NGC 1068, which was included
in the source catalog search. The excess at the coordinates of NGC 1068 is
inconsistent with background expectations at the level of $2.9\,\sigma$ after
accounting for statistical trials. The combination of this result along with
excesses observed at the coordinates of three other sources, including TXS
0506+056, suggests that, collectively, correlations with sources in the
Northern catalog are inconsistent with background at 3.3$\,\sigma$
significance. These results, all based on searches for a cumulative neutrino
signal integrated over the ten years of available data, motivate further study
of these and similar sources, including time-dependent analyses, multimessenger
correlations, and the possibility of stronger evidence with coming upgrades to
the detector.
