Critters are mobile non-player entities, typically small or non-predatory animals or vermin, intended primarily for ambiance.
While critters are a kind of mobile object, in World of Warcraft, "mobs" differ from critters in that critters are primarily for ambiance, provide no direct experience and little or no loot, and are trivial to kill. There are subtle mechanical differences, such as critters cannot be targeted by use of the tab key.
Any 'attack' that causes no damage will not kill a critter.
Many critters have just one hit point and always die when hit by a damaging attack.
Some critters have a few hit points and will survive a weak attack.
Size is a poor indication of relative robustness.
Many larger critters, such as deer and sheep, have one hit point.
Squirrels, which are among the smaller critters, have eight hit points.
Critters are (mostly) harmless and low level.
Most will run in fear if they survive the first attack.
Some critters, such as the rats in Deadmines and the Deeprun Tram, the Biletoads in Wailing Caverns, or Frogs (no, really!) will strike back at an attacker if the attack doesn't immediately kill them. They do minimal damage.
Priests can use Shadow Word: Pain to test critter reactions, as it has a delay before it does actual damage.
Many dungeons have critters in them, and dealing damage to them will generate rage for Warriors and Druids, making them usefull "rage batteries" (if there are multiple rage-users, just remember that the tank has priority).
DisciplinePriests can similarly use them to keep up their evangelism buff by smiting them (tank still has priority, but healer is second).
Before Patch 3.2.0 (although it was not mentioned in the patch notes - the effect just occured) critters such as Sheep, rabbits , Gazelles, and Deer were able to be skinned. As of Patch 3.2.0, they can no longer be skinned.
Amusingly, sheep can be polymorphed into sheep. The visual effect looks like dust billowing from the sheep.
Growl causes critters to run in fear instead of coming at you (although see above note about critter aggressiveness).
Many small pets share the same 3D model with the critters of the same type.
Many critters have an older, generic representative of the type, and representatives with more specific names added with new content.
Some critters represent a type of creature that is also or is primarily represented by mobs; spiders for example.
Some critters are quest objectives and achievement objectives.
Whenever a critter is the object of a quest or achievement, the name must match exactly.
Notes
The chicken critter is the only source of the [Westfall Chicken] small pet. During the course of obtaining the small pet, the chicken becomes an exception to the rule that critters are neutral, becoming friendly to characters, but at that point the chicken appears to be a temporary NPC, not a critter. Horde characters need to buy the special chicken feed from the neutral AH before they can do this.