Pulse sequences, designed to be insensitive to flow, e.g. at every even echo, a spin echo sequence is not flow sensitive. Velocity compensation is achieved by using gradients, which are either symmetrical around a 180° pulse and switched on twice as is the case for motion compensated spin echo pulse sequences, or two antisymmetrical gradient lobes without 180° pulse, which is the way to produce a velocity compensated gradient echo pulse sequence.
The signal of the second echo (and all other even echoes) is independent of the velocity of the object. Thus, velocity-based motion effects stemming from the entire voxel or from spins within a voxel (intravoxel incoherent motion) are suppressed with such pulse sequences.
If higher order motion is relevant, as it may be in turbulent jets across valves, acceleration and jerk effects can also be compensated for by the use of appropriate combinations of gradient- and radio frequency pulses.
With the increasingly stronger gradients, echo times in MR systems can be shortened to the point at which effects other than velocity effects hardly ever become relevant.

Quick Overview
Please note that there are different common names for this artifact.

This artifact is caused by movements of the patient or organic processes taking place in the body of the patient. The artifact appears as bright noise, repeating densities or ghosting in the phase encoding direction.

There are different solutions for reduction of phase encoded motion artifacts.
Cardiac and respiratory gating, breath holding, sedation of the patient, presaturation pulses for flow artifacts (e.g. arterial pulsation, breathing), fast imaging sequences, etc.

See also Motion Artifact, Ghosting Artifact, Motion Compensation Pulse Sequences and Artifact Reduction - Motion.

An image artifact is a structure not normally present but visible as a result of a limitation or malfunction in the hardware or software of the MRI device, or in other cases a consequence of environmental influences as heat or humidity or it can be caused by the human body (blood flow, implants etc.). The knowledge of MRI artifacts (brit. artefacts) and noise producing factors is important for continuing maintenance of high image quality. Artifacts may be very noticeable or just a few pixels out of balance but can give confusing artifactual appearances with pathology that may be misdiagnosed.
Changes in patient position, different pulse sequences, metallic artifacts, or other imaging variables can cause image distortions, which can be reduced by the operator; artifacts due to the MR system may require a service engineer.
Many types of artifacts may occur in magnetic resonance imaging. Artifacts in magnetic resonance imaging are typically classified as to their basic principles, e.g.:
Several techniques are developed to reduce these artifacts (e.g. respiratory compensation, cardiac gating, eddy current compensation) but sometimes these effects can also be exploited, e.g. for flow measurements.

See also the related poll result: 'Most outages of your scanning system are caused by failure of'

Flow compensation is based on the principle of even echo rephasing and a function of specific pulse sequences, wherein the application of strategic gradient pulses can compensate for the objectionable spin phase effects of flow motion. Gradient moment nulling of the first order of flow is another adjustment for the reduction of flow artifacts.
Gradient field changes can be configured in such a way that during an echo the magnetization signal vectors for all pixels have zero phase angle independent of velocities, accelerations etc. of the measured tissue. The simplest velocity-compensated pulse sequence is the symmetrical second echo of a spin echo pulse sequence.
Strategic gradient pulses are integrated in special sequences (e.g. CRISP, Complex Rephasing Integrated with Surface Probes) and for the most sequences flow compensation is an optional parameter.

Quick Overview

Ghosting artifacts are in the most cases caused by movements (e.g., respiratory motion, bowel motion, arterial pulsations, swallowing, and heartbeat) and appear in the phase encoding direction.

Ghosting artifacts can be reduced by respiratory and cardiac triggering, the use of breath holding pulse sequences, flow compensation or presaturation pulses, depending on their origin. To reduce bowel motion also pharmaceuticals, such as glucagon or scopolamine are useful. This will decrease artifacts from both peristalsis and breathing.

See also Motion Artifact, Phase Encoded Motion Artifact, Cardiac Motion Artifact, and Artifact Reduction - Motion.