A couple weeks ago Volokh blogged about 'thee' and 'thou'. One thing he mentioned that I've known for a little while but seems so contrary to popular opinion is that 'thee' and 'thou' were the informal and more personal versions of the second person pronoun, and 'ye' and 'you' were reserved for more formal situations. The informal 'thee' and 'thou' eventually became archaic, and their association with old-fashionedness, which also somehow got associated with formality, led to the dominant myth that 'thee' and 'thou' are more formal.
Should people use these terms when praying? Should people prefer a Bible translation that uses them with respect to God? I've encountered a number of people who prefer them and some who insist on it. I've also encountered probably a much greater number who have preferred 'you', many of them insisting on it. The issues become quite complicated, simply because most people don't understand the history of their own language enough to know why these words were chosen in older translations (and the archaic on this matter NASB) when referring to God.
Some people like the older language precisely because they share the same false assumptions and also think our relationship with God should be entirely formal. I hesitate to criticize them for that attitude, but it undermines Jesus' command to pray to God as Father, translating what was almost certainly 'Abba'. From what I've read, 'Abba' is less formal than 'Father' but a good deal more formal than 'Daddy'. There was a more formal term for a father that Jesus could have used. So the loss of familiarity is not just historically naive but theologically unmotivated.
Other people like the older language because they do understand that these are the more familiar terms and prefer to retain a distinction between the formal and informal second person pronouns, seeing rich theological meaning in the use of the informal when referring to God. This is a reason I can understand. These terms don't have this significance for me, simply because I was raised under the myth of their formality. I sympathize with their lamentation over the loss of such distinctions in pronoun use, but it is that -- a loss. We don't have it anymore. Resisting by trying to continue their use in religious settings isn't going to stop or reverse the fact of language change, and it isn't going to add that meaning that just isn't there for most hearers.
Because this fact about most Americans, I wonder if it's even a good idea to reserve such use for private prayer or prayer among others whom you know have the same understanding. After all, public prayer is not just talking to God. Otherwise it wouldn't be public. It's talking to God in the hearing of others, whom you expect will join in your prayer. It also provides an opportunity for more mature believers to model good prayer, with hard work on how public prayer can teach people to focus on biblical categories and teach biblical truth in the process. How can people join in my prayer unless I explain the significance of the terms? How can we teach them spiritual principles about our relationship with a personal God if we mislead them by communicating unintentionally that we distance ourselves from this God by our use of what they see as archaic, formal terms?
For that reason, I think public use of these terms for God is not a good idea. Still, it irks me to hear people complaining about it. Usually such complaints come from a mindset that only the last few years of Christian existence are good, seeing most of the two-thousand years of God's people, of the work of the Holy Spirit through history, as worthless and not for us. This shows up in the hymn-hating mindset of our day, among other places, and if the opposition to 'thee' and 'thou' is simply for this sort of reason, then I want no part of it.
Of course, it irks me even more when people use 'thee' as a subject or 'thou' as an object. It shouldn't but there's a good rule of thumb to follow when wondering if something irks me. If the three following characteristics are true, then it's a safe bet that I'm annoyed:
(1) Someone's usage is wrong.
(2) I know that it's wrong.
(3) I know that they used it that way.
My knowledge of correct grammar is fairly extensive, and I have a mind for such details, so the second and third conditions are almost always true when the first is and I'm nearby. I try not to let this affect me too much, because I know the earlier issues are vastly more important, and it's kind of silly to be correcting people all the time or trying to make them look stupid by pointing out insignificant things.
Also, I'm well aware of and convinced by linguists' arguments that some usage mistakes have become standard spoken English, so just because something is wrong in standard written English doesn't mean I think it's wrong in spoken English. Not all common mistakes are of this sort, though. The ones that really annoy me are when people think they're going out of their way to say it right but still get it wrong (e.g. "Jeremy and myself are doing such-and-such" or "Give it to Jeremy or myself" or "Give it to Jeremy or I"). It's annoying to insist in spoken English that we abide by the rules of formal written English, but it grates on me even more when people think they're high-and-mighty enough to be modeling such behavior but actually getting it wrong!
Well, I think I've said enough to offend almost everyone, including me, so I'd better stop.