A listing (which is fairly inclusive, but might not be complete) of “Independent Establishments and Government Corporations” can be found at http://firstgov.gov/us_gov/establishments.html These span a broad spectrum of agencies - and most people will probably find some of their favorite government agencies AND some of their prime examples of governmental abuse on the list. It includes (in alphabetical order, to take some of the most famous) the Central Intelligence Agency, the Environmental Protection Agency, the Federal Communications Commission, the Federal Deposit Insurance Commission, the National Endowment for the Arts, NASA, the National Science Foundation, and much more.
IIRC These organizations are referred to as “independent” NOT because they are immune to control by political processes, but because they are not formally a part of any of the fourteen executive departments (State, Defense, Treasury, Commerce, etc.) Most of them are still subject to a variety of political controls.
The commissioners are appointed by the President. While many of the terms are fixed (so that GWB will have to live with some of Bill Clinton’s commissioners for a while yet) - for most of these parts of the government, there is another vacancy each year, and the total number of commissioners is small enough that a President will typically have appointed a majority before the end of his (or her) first term. In addition, the President will be able to name people to fill vacancies, and for many of these there are likely to be a few vacant positions at any given time. In some cases, the President can fire sitting commissioners, which also gives him/her opportunities to change the agency’s leadership.
In addition, most of these agencies do require annual budgets - which means that they must go through both Executive and Legislative branch budgeting processes. This can also be a substantial check on their authority and discretion.
The Federal Reserve has seemed particularly free of political control for some time - but I would argue that this is at least as much a reflection of the political skills of Alan Greenspan and the political clout of his supporters as it is due to the formal organizational structure of the Federal Reserve Banking System. By this point, any president who attempted to appoint a different chairman would face enormous political and economic problems regardless of who the replacement was. Fundamentally - Greenspan seems to me to be in many ways quite comparable to J. Edgar Hoover in terms of his ability to maintain a position in the Executive Branch relatively free of political controls. (The REASONS they maintain that power are quite different, I hope, but the autonomy each has seems similar). Hoover, as head of the FBI, was in the standard agencies (FBI is a part of the Justice Department).
My own take would be to say that there is not any strong evidence right now that the independent agencies are any more, or less, problematic than any other part of government. Some have done well, some have been abusive. They have been more popular recently (over the last 50 years or so) as a way of structuring new activities by the Federal Government, but it is not clear that this way of setting things up makes a huge difference by itself.