Aggro radius

The aggro radius is the distance from a player at which a mob will stop its idle behavior and engage the player in combat (see aggro). It is primarily determined by the level difference between the monster and the player character.

Level-based behavior
The aggro radius of a mob will vary depending on the level difference between it and the player character. The higher the level of the character compared to the mob, the closer the player can get without being attacked. Very high level characters can often run through densely occupied areas without being attacked at all, although there appears to be a minimum radius that will always get the player noticed, regardless of level superiority. On the other hand, low level characters accidentally wandering into or intentionally traveling through a higher level area can often be surprised when they are attacked by mobs so far away that they were not even noticed.

For this reason, when a high level character (Hiram) is helping a low level one (Leeroy), Hiram must be aware of areas that would be safe for himself but not for Leeroy, and should keep an eye out to aggro or kill any monster that ignores himself and attacks Leeroy. Leeroy, similarly, should not automatically assume safety in an area just because Hiram made it through without being attacked.

Co-aggro
If a player (Paula) is in combat with a mob (Commando), and Commando ends up within the aggro radius of a second mob (Security) that is currently not in combat, then Commando may pass on his aggro to Security, and Security will be added to the fight. Security will initially have a threat of 0 against Paula, but will still attack her unless someone else gains higher threat. Situations when this is likely to occur include Paula attempting to run from Commando, using Fear effects on Commando, rooting Commando and then repositioning poorly, or when Security respawns or patrols close by to Commando. "Fear aggro" is particularly common and dangerous in dungeons, since the fear direction can be unpredictable, monsters tend to be packed in clusters, and most will chase indefinitely. Any of the above are even more likely if Paula jumps up or down a ledge over which Commando cannot follow, forcing him to take an unpredictable path to pursue her.

Co-aggro is very likely to occur when the two monsters are of the same faction or creature type. A Bloodsail pirate will always co-aggro nearby Bloodsail pirates, but will probably not co-aggro a gorilla. NPCs that are friendly (green) to the player will never be co-aggro'd, but NPCs that are neutral or unfriendly (yellow or orange) - who would normally not attack the player for entering their radius - may be co-aggro'd.

Non-radius-based aggro
Related to co-aggro is group aggro, where a predetermined group will all aggro Paula if she attacks any of them, regardless of radius. Sometimes the group aggro is not symmetric - for instance it may be impossible to pull an elite monster without aggroing his "friends", but possible to pull a friend away from the elite using ranged attacks without engaging the whole group at once. This is particularly common in instances, where engaging a boss typically aggro's any remaining mobs in the room, but not vice versa.

Finally, certain monsters may have a "shout" ability that aggro's other monsters within a large area, regardless of the others' aggro radii. These can sometimes pull bosses prematurely and are dangerous with any nearby monsters at all, so such monsters should be crowd controlled and interrupted until dead.

Formula
Current in-game testing shows the following facts:
 * The aggro radius of a mob having the same level as the player is roughly 20 yards (~ 18 meters)
 * Aggro radius varies with level difference at a rate of roughly 1 yard/level.
 * Minimum aggro radius for a mob seems to be combat range (5 yards).
 * A Hunter's pet seems to ignore the minimum aggro radius for low level mobs, even when controlled through Eyes of the Beast.
 * Aggro radius is capped at a maximum of 45 yards, that is, when the mob is 25 or more levels higher than the player.
 * Vertical distance seems to be weighted much more heavily than horizontal distance. A mob standing on a ledge 4 yards above your head can fail to aggro even if standing 4 yards away from the same mob on level ground will draw aggro.

Speculation

 * Some mobs appear to have higher aggro radius against stealthed players. Examples would be Gordok Mastiffs in Dire Maul (north), and the bloodhounds in Blackrock Depths. This may be a matter of exceptionally good stealth detection rather than an increased aggro radius, however. --Confirmed to be stealth detection now that stealth detecting mobs have a symbol above their head.
 * Some mobs appear to have higher aggro radius than expected for their level against all players. The Warpwood Crusher in Dire Maul (east) has a much higher than normal aggro radius. Against level 70 players, their aggro radius seems to be reduced as would be expected when compared to a level 60 player, but the aggro radius is still far larger than would be expected for a typical level 56 elite mob. Casual testing estimates 1.5-2 times the normal aggro radius of a similar level mob.
 * The aggro radius around a mob does not appear to be angle-independent: The distance at which a player will draw aggro while standing in front of a mob tends to be greater than the distance at which the same player will draw aggro while standing behind the mob. This may, however, be because the mob is often walking forward, and the location of the mob reported to the WoW client will lag a fraction of a second behind its actual location on the realm server. It may also be because the actual location for a mob may be forward of the center of its body (e.g. the "hit box" for a wolf is centered on its head, not on the center of the red targeting disc). Chances are however that this is intended behaviour, and in-game situations suggest this is a real effect not (only) caused by the mobs moving forward.
 * The assist radius of a mob (the distance within which another mob friendly to the aggroed mob will also aggro) seems to be different from the aggro radius in many cases.
 * Mechanical mobs in general (though not always) seem to have a slightly higher aggro radius than other mobs their level. The mechanical golems in Westfall, for example, seem to be much more aggressive than normal.
 * Mobs with the word "starving" in their name (Starving Dire Wolves in Duskwood, Starving Blisterpaws in Tanaris, etc.) also seem to have a higher aggro radius than other mobs, presumably because they are starving. The Starving Dire Wolves (levels 19-20) appear to aggro from further away than the nearby Rabid Dire Wolves (levels 20-21), the Starving Blisterpaws appear to aggro from further away than the nearby similarly leveled buzzard and scorpid mobs, and so on. Exercise caution around starving mobs.

False speculations

 * Some people say that different classes have different aggro radius against different types of creatures (e.g. Hunters can come closer to Beasts without aggroing than other classes). This is false, though it is based on truth. There was a period in early beta during which this was the case.