Quotes ( " " ) are used to mark something that somebody has said, or something that is phrased in this exact manner, in computer-type usage, to contain a "string" (a group of letters organized in a certain fashion), to denote a perhaps unfamiliar word (or a familiar word used in an unfamiliar way) that is to be defined, or to be used with a certain definition other than the standard, or in the talking of items or activities that can be described as "alleged" or "so-called".
For example, President Dubya Bush has been "peacemongering". In this context, the use of quotes around "peacemongering" is to indicate that the way that the word is being used really means that he's been talking about blowing the hell out of Saddam, and is unlikely to be changing his mind no matter what his advisors or the American public say.
Pet peeve: when people use quotes instead of italics, bold, underlining, or other forms of emphasis.
Take a look at these two sentences:
I really don't like peanut-butter and jelly sandwiches.
I really "don't like" peanut-butter and jelly sandwiches.
In the first sentence, with the phrase "don't like" in italics, the meaning is clear: the not liking is not a mild feeling, but a strong one: I hate them! I really do! I wouldn't touch them with a ten foot pole!
In the second sentence, with "don't like" in quotes, the way that I must think of this is that "don't like" is a special, perhaps sarcastic or ironic use of the two words, not meaning the standard. Perhaps I absolutely love them, and I'm saying this while rolling my eyes, and after I finish saying this, I will snicker, because everyone knows that I love PBJ; the best birthday gift you could get me is one of those jars of the striped PBJ stuff, because I won't eat anything else.
There is one usage where the use of quotes and italics overlaps. If I'm talking about a word, or a short phrase, whenever I mention it out of its usable context in a sentence, I have to mark it to my reader somehow so they won't get confused about what I'm saying. In this case, it is perfectly acceptable to italicize the word in question.
Today's word is perdurable.
Today's word is "perdurable".
Today's word is 'perdurable'.
It's generally confusing, but the simplest rule to remember to avoid making my editorial ears steam is this: Emphasize using <i> and </i>!