Let me begin by saying that I love my TI-83+ with all my heart. We've been through a lot together -- the SAT four times over, the Calc AP test, the GRE, and oh yes, my entire undergraduate career in the sciences. I credit it for keeping me sane in high school chemistry, both with the molar mass program I wrote to easily calculate the mass of any carbohydrate and with the 5-card-stud poker program I used to zone out of particular easy lectures. After 9 wonderful years, the poor thing is showing signs of being on its last legs; I am devastated in the same manner as a small child whose favorite toy has broken. So strong is my devotion to the 83+ that, when it comes time to purchase a replacement, I would eschew the [admittedly much sexier] TI-89 without a second thought if I was certain that the students I will eventually teach would still be using the now-comparably-ancient 83+.
And I don't think they should be used in a classroom.
My view is that calculators should really only be allowed in class for tasks that would waste inordinate amounts of time and paper otherwise, such as basic operations on large numbers (e.g. 674.5 times 325.2). Allowing them for use in all scenarios causes students to rely on them too heavily, to the point where "obvious" math problems such as 12/1 or 15x0 cannot be seen without the aid of a liquid crystal display. Concepts like this are central to an understanding of math, and while the calculator is just one of many tools for solving a problem, it does little to aid the understanding.
The issue that I come across is that my personal rapport with the 83+ comes from years of experience and an innate knowledge of how I need to input any particular expression. Say, for example, that you wished to find the square of -2. On the scientific model TI-30, you input the 2 first, then press the negative sign, then hit the x² key (or x^y, then 2, then enter). However, on an 83+, it's a different beast entirely: open parenthesis, negative sign, 2, close parenthesis, x² key (or ^2). Without this exact combination of keys, odds are good that you will be getting -4 as your answer.
And many students will submit -4 as their answer without a second thought, since they are certain that the calculator will always find the correct answer. It has no reason to lie. This blind trust is the great tragedy of calculator usage. The calculator will always do the math perfectly, but it requires that the user also be perfect with the input of the question. To this end, teachers must devote entire blocks of time to the instruction on how to input the expression into a calculator, rather than focusing the discussion on why the answer comes out the way it does.
I understand that calculators, like the algorithms we use to solve expressions, are merely tools that humans use in order to definitively calculate the relationships between numbers. My issue comes with the fact that the calculator is a tool which requires that the user master it first before the user can move on to mastering the skill it is supposed to help with. (The issue is compounded further if a student replaces their calculator with another model, forcing them to develop the skill set of proper calculator usage all over again.)
For understanding things like zeroes of a function, maxima and minima, and other tools which are useful when seen graphed in the context of an algebra-2-and-higher setting, I agree that calculators can be a great help in furthering knowledge. Essentially, I suppose this means that I am a fan of calculators when they're not being used as calculators, and instead as things such as graphing or trigonometric tools. Until then, I don't feel that the use of calculators in a classroom adds anything to the student's basic understanding of math. It may save the student time, but it also saves them from having to think about what is truly being done.
