The Player's Handbook on the ranger's extraordinary ability favored enemy says
At 1st level, a ranger may select a type of creature from among those given on Table 3–14: Ranger Favored Enemies. Due to his extensive study on his chosen type of foe and training in the proper techniques for combating such creatures, the ranger gains a +2 bonus on Bluff, Listen, Sense Motive, Spot, and Survival checks when using these skills against creatures of this type. Likewise, he gets a +2 bonus on weapon damage rolls against such creatures. ...If the ranger chooses humanoids or outsiders as a favored enemy, he must also choose an associated subtype, as indicated on the table. If a specific creature falls into more than one category of favored enemy (for instance, devils are both evil outsiders and lawful outsiders), the ranger’s bonuses do not stack; he simply uses whichever bonus is higher. See the Monster Manual for more information on types of creatures. (PH 47)
There's nothing there about immunity to critical hits or precision damage. And, after the chapter on skills, there's nothing in the Player's Handbook about the extraordinary ability favored enemy. (The Monster Manual mentions the special ability favored enemy only by listing some creatures' preferences.)
The Rules Compendium on Precision Damage says that precision damage
includes sneak attack and other abilities that work like it, such as a ninja’s sudden strike (Complete Adventurer 8) and scout’s skirmish (Complete Adventurer 12). (42)
And, seriously, the extraordinary ability favored enemy doesn't work like those special abilities. (Besides, why use an example from Complete Adventurer when there's a fine example in the Player's Handbook that can be used instead? That's just weird, right?)
However, the Dungeon Master's Guide mentions the special ability favored enemy in the context of Invisibility:
Invisibility does not, by itself, make a creature immune to critical hits, but it does make the creature immune to extra damage from being a ranger’s favored enemy and from sneak attacks. (295)
And, likewise, in the context of Darkness:
Creatures blinded by darkness lose the ability to deal extra damage due to precision (for example, a ranger’s favored enemy or a sneak attack). (302)
This leads to the question: Is the ranger's favored enemy bonus on damage precision damage or just a bonus on damage against certain creatures? That is, are creatures immune to critical hits likewise immune to the ranger's extra damage from the extraordinary ability favored enemy, or can a ranger, for example, pick as his favored enemy the creature type construct, elemental, ooze, plant, or undead as a favored enemy and against such creatures always apply that favored enemy bonus on damage to such creatures?
What I'm really trying to hammer out is the epic feat Improved Manyshot, which says
Regardless of the number of arrows you fire, you only apply precision-based damage (such as sneak attack damage or the ranger’s favored enemy bonus) once. If you score a critical hit, only one of the arrows deals critical damage (your choice); all others deal normal damage.
Emphsis mine. So addressing this feat specifically makes an answer more useful. Also, whenever I ask a question that I think only has two answers, there're inevitably more, so if you've an answer that goes unaddressed here, that's okay. Finally, while I understand the rules for primary sources and that the feat Improved Manyshot can't alter them, the conflict between the Player's Handbook and the Dungeon Master's Guide nonetheless concerns me.