What's the difference between the following sentences?
(a) I wish they wouldn't make so much noise.
(b) I wish they were not making so much noise.
(c) I wish they did not make so much noise.
I'd appreciate your help.
Sentence (a) means that you wish they were willing not to make so much noise on some occasion or occasions not specified within the sentence.
Sentence (b) means that you wish that they were not right now making so much noise.
Sentence (c) means that you wish that it was not their habit to make so much noise on some occasion or occasions not specified within the sentence.
For me, all three sentences mean the same. Irreal wishes can be expressed with "wish" (Present Tense) + Past subjunctive or would (Conditional 1).
I wish father were* here. (were*: the asterisk marks the genuine past subjunctive)
In colloquial language you can say: I wish father was here. (this "was" has the character of a subjunctive)
I wish it would rain. (In colloquial language the tense with would can be used, especially with regular verbs.
Remark: It is a specialty that English uses the Present Tense I wish, whereas in German one would say: Ich wünschte or Ich wollte.
When you use "would" you say I would father were* here. / Would father were* here.
It's not quite so clear-cut in practice as StoneyB's answer might seem to imply, since the meanings do overlap a bit.
Starting from the end, your sentence (c) is, in my opinion, the most common and idiomatic of the three. It does not specify when you "wish they did not make so much noise", and therefore can apply equally well to either ongoing, recurrent, future or even hypothetical events. (For a past event, you could instead say "I wish they hadn't made so much noise.") In particular, sentence (c) could be validly used to replace (a) or (b) in pretty much any context I can think of.
Your sentence (b) uses the present participle, and therefore specifically refers to an ongoing action (that is, some people making noise right now, and continuing to do so). It cannot be used to refer to noise that you expect to occur sometime in the future, or that occurs regularly but is not happening right now.
Finally, your sentence (a) uses the verb "would", which can be used for two different purposes in English: either to indicate choice or intent on someone's part, or as an auxiliary verb to form the conditional mood. I would argue that, depending on context, either interpretation is possible:
The first interpretation ("would" indicating choice) requires "they" to be a person or other conscious agent capable of choosing whether to make noise or not. When used in this sense, your sentence (a) could be rephrased more literally as:
(a*) I wish they did not choose to make so much noise.
However, at least to my ear, the expression "wish [they] wouldn't" could also be used in some situations where the subject is clearly inanimate and incapable of making a choice, as in:
(a**) I wish my car wouldn't make so much noise when I start it.
In this sense, the sentence is essentially equivalent to your sentence (c), except that using "wouldn't" instead of "didn't" makes the whole sentence more hypothetical: "I wish they wouldn't make so much noise, but they probably will anyway."
Ps. Note that the negation in your example sentences is pretty much irrelevant; you could just as well have phrased them as:
(a') I wish they would make (less) noise.
(b') I wish they were making (less) noise.
(c') I wish they made (less) noise.
and the answers would have been essentially the same.