As often in an ox fight, it depends on whose ox is being gored.
There has been an attempt on a number of school campuses to restrict “hate speech” with the original worthy intention of reducing the amount of verbal intimidation that some students could inflict on others. This has led, in some cases, to utterly absurd situations. (The "niggardly"example, above, is not so much a case of Political Correctness as sheer ignorance. Nigger is a hateful term and mistaking niggard for nigger is an example of abysmal ignorance.) However, there have been genuine cases of PC run amok, as in the case of the Penn State student who was reprimanded for calling a bunch of boisterous drunks “water buffalo” when he was a white male and the drunks were black females. (This led to some really strained attempts by some twits to create a “racist” epithet out of a word that had no history of racial connotations, hurled at loud drunks–giving opponents of PC legitimate ammunition in some cases for their outrage.)
In these cases, PC is generally a negative term applied by the Right (with some reason) to language issues raised by the Left.
On the other hand, in some cases, PC is nothing more than consideration, as noted by Hugh Jass. There have been any number of insulting terms for various people that are no longer used in polite society. Ethnic slurs, referring to women (especially in a professional capacity) as “girls” or “broads,” dismissive terms based on physical disabilities, referring to homosexuals as faggots or dykes: all these have been put under tabu. (Claims by the bigots on the Right that we are “not allowed” to use some terms are, of course, nonsense. While the terms African-American and Native American are preferred by some people, the terms black and Indian are actually preferred by majorities of the people who could be so identified and claims that we “can’t” use those words are hysterical whines (generally from people who would prefer to use nigger and redskin).)
On the other hand, the Right has its own form of political correctness (which actually preceded the Left’s PC) that generally involves making tabu any negative references to actions that are not perceived as suffiiciently patriotic or religious. We simply have not yet come up with a scathing term for the Right’s censorship.
In some cases, there are claims made against PC that are, themselves, utterly stupid. A number of terms for people with physical or mental handicaps have undergone a continuous process of re-invention, with successive terms used in an attempt to remove the stigma associated with the earlier terms. This attempt to find non-pejorative terms extends back into the nineteenth century and long preceded the Political Correctness movement that only got going in the mid to late 1970s. When someone moans because they can no longer call a person with Down Syndrome “dummy” because it is not “politically correct,” they are not merely abusing the phrase “politically correct,” they are displaying an abysmal ignorance of the changes in language that preceded the PC movement. (On the other hand, I will note that the contiuous process of changing terminology is pretty much a waste of time and energy. As soon as “mentally challenged” was put forth as a term, it immediately became a joke phrase used to mean “stupid.” Years and years ago, the slowed development of some people was noted in their “retarded development” which almost instantly became the playground catcall, “REE-taaaard!”)
Some PC is politeness and some PC is an attempt at “mind control.” There is not a single answer to cover every application, because so many people use the phrase to mean different things.