We present 15 GHz VLA observations of the M87 jet at six epochs spanning 1982 to 1993. Comparison of these images reveals outward motion in five of the brightest knots. Typical apparent speeds are near 0.5c (where c is the velocity of light), although knot C near the jet's terminus is significantly slower. Within the knots, individual features often show a large range in speed. Small features within knot D, which is nearest the nucleus, show superluminal speeds up to 2.5c±0.3c. Motions transverse to the jet axis are also seen. The misalignments between the velocity vectors and jet axis become especially large near the end of the jet where it appears to bend and oscillate from side to side. Constraints derived from the observed motions, as well as the appearance of a sharp edge in knot A, suggest the jet is oriented about 43° from the line of sight. We outline a kinematic model for the jet wherein the first kiloparsec consists of a relativistic flow (γ ≳ 3) followed by deceleration in knots A and C. Such a picture can account for important properties of M87 and other F-R I radio sources.