For some reason I've been thinking more about Clerics lately, and why I don't use them. I thought I'd jot down my reasons. Feel free to comment.
Miracles and Levels: Probably my biggest beef with Clerics is that their God/gods will help them, but only so much. I don't see why, if it's the deity's power and not the Cleric's, the power should get stronger and more effective as the Cleric levels up, unless we've got a really fickle deity here. It seems like a deity would say "hey, there's this guy that's much more dedicated to me than the average person down there, and I usually help him out when he asks, so why not grant whatever it is that he's asking me, seeing as how it totally aligns with what I'm about?" If spells and turning undead are really just the power of the deity, why does this change as the character changes?
I realize that a lot of this thinking comes from my Christian background. While a lot of miracles in the Bible are the inspirations for D&D miracles, in the Bible miracles don't tend to get more amazing as the person they are associated with gets more experienced. Instead, miracles tend to meet the needs of the moment, demonstrate the unquestionable power and reality of God and also tend to be unique, as opposed to the reproducible formulae of D&D magic. Even in, say, Greek polytheism, though, miracles are questions of the god taking on the problem and aren't based on how "good" at something (or however we want to analogize levels to Greek myth) the character the miracle is done for is.
I also realize that there are mechanical reasons why this is the way D&D Clerics work. It just doesn't make sense to me so far as setting goes. Vancian magic and spell levels that go up as you level up just don't seem to fit the idea of a Cleric nearly so well as they fit the idea of Magic Users, in my opinion. Also, for mechanical reasons, having the Cleric able to get whatever miracle is asked for is out. For non-railroady reasons, making up my own miracles and making them happen whenever I see fit is also probably not a good idea, though it might be a possibility if it was done really well.
Undead: I don't use undead in my campaign, largely because it seems to me to make the divine in the setting inept. That is, why would a deity that doesn't want undead to exist need a mortal and a little piece of metal or wood to be present in order to keep something dead? I suppose that the undead might make sense if the setting's cosmology is strictly dualistic, with Good and Evil equally powerful, and I suppose the argument might be able to be made that much of D&D, especially AD&D and later, actually does have that dualistic cosmology, but I've no particular interest in running a game like that. Most people throughout history haven't held to a cosmology of Good vs. Evil, and especially not to an even match-up of Good vs. Evil, instead holding to the concrete personhood of whoever they worship and in that deity's dominion over however much of the world they believe their deity controlled. Good vs. Evil as THE story of the universe is a pretty rare way to look at the world, and one I'm not interested in, both because I don't believe in it and because I've seen some of the evil (yes, I do believe in good and evil, just not that they are THE lens to see the world through) that can occur when people do see the world that way and I don't want to encourage it.
Healing: This is really more of a mechanical disagreement than a question of me "getting" the Cleric. I don't like healing being the exclusive domain of any one class, mostly because I don't want either that class to be seen as a "healbot," nor do I want players to feel that one of them needs to be that particular class so that healing can occur. That's why I've let classes like Barbarians and Rangers in the past and Scoundrels in my current game be able to heal. It's also why I use the rule that minor healing can occur for every character immediately after a combat is over, by way of first aid. This doesn't exactly make the Cleric worthless, as Clerics could be just another class that has healing abilities, but it also makes them less special.
So, in conclusion, if I have a problem with divine magic being tiered with levels, the existence, as well as the turning, of undead, and have given healing to other classes as well, the Cleric ends up looking like a really pious Fighter who doesn't fight as well as the Fighter, so it doesn't make a lot of sense to include them in my games. I know this is a very minority opinion, though, and I am truly interested in comments from people who do like and use clerics.