Non-living
Non-living and unliving are terms that refer to creatures that have never been alive. They cannot be affected by mind spells and spells that require a living target, and they have neither positive nor negative morale. The term non-living was introduced in the The Shadow of Death manual, the only use of non-living in the manuals (used to describe creatures unaffected by the Elixir of Life). Unliving is not used at all in the manuals but replaces non-living in the in-game description of the Elixir of Life.
Stone gargoyle and obsidian gargoyle are also considered non-living, but they are still affected by morale and mind spells. 
In Horn of the Abyss, they are called "Bloodless" instead of non-living.
Although war machines as units on the battlefield can be considered non-living in some sense, they have their own system of immunities.
Crystal dragons are described as being "made entirely from red crystal and brought to life through magical means..." and are referred to as dragon golems in the campaign. Despite these references they don't have any features that would set them apart from any other living creatures.
NOTE: For comparison, living units are just units that are NOT non-living and NOT undead. See Undead vs Unliving for more explanation.
Non-living creatures
Golems
The only common trait of golems among all other non-living creatures is spell damage reduction.
Elementals
Air and Storm Elementals
Water and Ice Elementals
Fire and Energy Elementals
Earth and Magma Elementals
Psychic and Magic Elementals
Gargoyles
Unlike other non-living creatures, gargoyles are still affected by morale and mind spells. In Horn of the Abyss, they are called "Bloodless" instead of non-living.
Mechanicals
Mechanicals have identical attributes as other non-living creatures, but can be repaired by Mechanics and Engineers.
Immunities
Spells
Mind spells (except for gargoyles)
Creature abilities
Azure Dragons: ● fear
Ghost Dragons: ● aging
Lich and Power Lichs: ● death cloud
Mighty Gorgons: ● death stare
Pit Lords: ● summon demons
Vampire Lords: ● life drain
Wyvern Monarchs: ● poison
Zombies: ● disease
Sea Serpents and Haspids: ● poison
Artifact effects
Elixir of Life: ● regenerating, 25% health bonus
Horn of the Abyss: ● Fangarm summon
See also
1800
4696 
3000
1
525
600
600
140
170
500
100
125