I've had a vague idea on how to ditch clerics without losing their functionality, and the recent blogosphere murmurings about the cleric -- at Trollsmyth and RPG Blog II, for example -- have prodded me into acting on those ideas.
First, in my opinion, cleric abilities are keyed to Law. This may seem shocking to those used to the way alignments and religion have evolved in D&D, but I think the original rules kind of hint that clerics can't be neutral and Chaotic clerics (anti-clerics) are actually more like medieval concepts of Satanists than an actual religious faith. The cleric is devoted to strengthening the community through faith in a higher power: essentially, a Lawful pursuit. The anti-cleric is someone who bargains with dark powers for power over the living and the dead. Druids, in keeping with the earliest versions of that class, are more like devotees of nature who have gained power over the wilderness through study rather than through faith, so these rules won't apply to them.
Second, following this idea, the ability to turn undead as a first level cleric could be made into a prayer mechanic for any character aligned with Law. Since turning undead was the original reason for the cleric class, this partially salvages their primary function.
Third, what about higher-level cleric ability? I'd make players sacrifice experience for increased turning ability: if a character earns enough experience to increase a level, the player can opt to increase cleric prayer ability to the next level instead, resetting experience points to the start of their current level. Call the cleric equivalent level "faith level". To get a faith level above 1, however, the character must seek out a temple and take a vow of some kind. I'd require a triple vow: no edged weapons (as per clerics,) tithe (as per paladins,) and something else, which could be open to discussion.
Fourth, what about healing and other clerical functions? I'd expand the turn undead ability to cover miracles (clerical spells.) A character can pray for a miracle, then use the turn undead mechanic to "turn" a creature with hit dice equal to the spell level of the equivalent clerical spell. Characters can pray for miracles as many times as they want, but their level of faith limits the number of miracles that will actually be fulfilled; use the clerical spell progression for the maximum number of miracles of each type.
Anti-clerics would work the same way, except that Chaotic characters are relying on their own force of will to enslave undead and must find a Chaotic supernatural power to pact with in order to get higher anti-clerical powers.
I would probably combine these rules with the piety rules to further control miracles.