Principles of grouping neurons
In anatomy/physiology, there are 2 major categorizations of the nervous system:


Central nervous system (brain + spinal cord) and peripheral nervous system (all other neural structures)
Somatic nervous system, which controls skeletal muscles and skin, and and autonomic n. system, which controls internal organs, blood vessels and glands and is further divided to sympathetic and parasympathetic system. Both the somatic and autonomic system have motor neurons that control muscles and sensory neurons that convey sensory signals. 




Image source: Wikipedia, creative commons license

Neurons can be further categorized by neurotransmitters involved (dopamine system, acetylcholine system, etc.), and by various anatomical and functional subsystems.

Examples of anatomical and functional structures formed by neurons:


Cortical areas (functional areas of the brain cortex) (Lumen)
Main parts of the brain: cerebrum, cerebellum and brainstem, some of which can be further divided into hemispheres, lobes and folds
Deep structures of the brain: thalamus, hypotalamus, hypocampus, amygdala, corpus callosum, limbic system, pituitary gland, pineal gland, and structures collectivelly called basal ganglia, which include the caudate, putamen, and globus pallidus in the cerebrum, the substantia nigra in the midbrain, and the subthalamic nucleus in the diencephalon (Mayfield Clinic). 
Areas containing either neuron cell bodies or axons: gray matter (cell bodies) and white matter (axons) of the brain and spinal cord (Indiana.edu)
Histological areas of the brain: layers and columns (Wikipedia)
Nuclei of the cranial nerves (Wikipedia)
Centers (cardiovascular center, reflex center for cough, vomiting, etc.) in medulla oblongata (Wikipedia)
Corticospinal tracts (Wikipedia)
Pathways - the term is usually used for cranial nerves: visual pathway, auditory pathway, etc.
Ganglia - anatomical structures containing neuron body cells in the peripheral nervous system (Wikipedia)
Nerve plexuses - branching networks of intersecting nerves (Wikipedia)
Reflex arcs (Wikipedia)