The Player's Handbook on the skill Intimidate says, "A character immune to fear… can’t be intimidated" (77). The Monster Manual on Fear says, "All fear attacks are mind-affecting fear effects" (309 and emphasis mine), but calls out only fear auras, rays, and cones as fear attacks. Further, the list of traits for creatures possessing the type undead says that such creatures possess "[i]mmunity to all mind-affecting effects (charms, compulsions, phantasms, patterns, and morale effects)" (317)—absenting from its parenthetical list fear effects (and, obviously, attacks).
The Rules Compendium on Fear Attacks says, "When they’re not spells, fear attacks can be extraordinary, supernatural, or spell-like, with specifics explained in the ability’s description" (53), yet employing the skill Intimidate to demoralize opponent isn't—so far as I can tell—a special ability.
Can a creature that possesses the type undead and an Intelligence score of at least 1 be the subject of Intimidate skill checks? Or is the typical lich or vampire, for example, simply immune to fear generally, including attempts by foes to employ against it any use of the skill Intimidate?
Note: I was reminded once again of this issue by the Shattered Gates of Slaughtergarde prestige class twisted lord (13–15) that has several special abilities that can only be used against a shaken foe. The typical twisted lord renders a foe shaken by employing the skill Intimidate to demoralize opponent, and two twisted lord abilities the lord can subsequently employ against a shaken foe aren't described as mind-affecting. If the twisted lord can demoralize, for example, a ghoulish troll or a warforged raptor or a fiendish gelatinous cube monk, the twisted lord gains a modicum of relief against foes he'd be otherwise at a loss to handle. I mean, sure, twisted lord remains a pretty sad prestige class (it's, like, four good levels in a 10-level package), but the idea of, for example, an unsleeping twisted lord who has successfully employed the supernatural ability twist mind on a lich and who subsequently keeps the lich around for kicks is mildly amusing (although probably not if you're a lich).
This question gets bandied about all over the Web (like in 2010, 2011, 2012, and 2012). Pathfinder addresses in its FAQ this exact issue (and this site in this question), but I'm unaware of a 3.5e source that addresses it similarly.