Newton's laws of motion were first published in 1687. They appeared in Philosophiæ Naturalis Principia Mathematica, usually called the Principia, Newton's landmark Latin work on mechanics and gravity.
The book was published in London on 5 July 1687. Edmund Halley encouraged Newton to complete the work and personally helped finance its publication after the Royal Society could not cover the printing costs. The first edition was followed by revised editions in 1713 and 1726.
Newton's laws were presented alongside his law of universal gravitation. Together, they provided a mathematical framework for explaining falling objects, collisions, planetary orbits, tides, and other motion. Newton also used the Principia to derive Kepler's laws of planetary motion from more general principles.
A common mix-up is confusing 1687 with 1727, the year Newton died, or with 1728, when an English translation of the Principia appeared. The laws themselves had earlier intellectual roots, but 1687 is the canonical publication year.