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.

Respiratory compensation reduces motion artifacts due to breathing. The approach is to reassign the echoes that are sensitive to respiratory motion in the central region of k-space. The outer lines of phase encoding normally contain the echoes where the motion from expiration is the greatest. The central portion of k-space will have encoded the echoes where inspiration and expiration are minimal. By a bellows device fixed to the abdomen, monitoring of the diaphragm excursion is possible. Respiratory compensation does not increase scan time with most systems.
An advantage of very fast sequences is the possibility of breath holding during the acquisition to eliminate motion artifacts. Breath hold is commonly used on most abdominal studies where images are acquired using gradient echo-based sequences during a brief inspiratory period (20-30 seconds). To enhance the breath holding endurance of the patient, connecting the patient to oxygen at a 1-liter flow rate via a nasal cannula has been shown to be helpful.
Also called PEAR, Respiratory Trigger, Respiratory Gating, PRIZE, FREEZE, Phase Reordering.

See also Phase Encoding Artifact Reduction, Respiratory Ordered Phase Encoding.