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When and how do we use the different kinds of brackets/parentheses — (){}[] — while writing English (not code)?

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Closing as too broad and for complete lack of research. Could be considered general reference as per en.wikipedia.org/wiki/Brackets. In fact the accepted answer just quotes select bits from that page, while leaving lots of things out. –  RegDwigнt Jan 19 '13 at 11:31
    
...Except my answer never did get accepted. Sadface =( –  Southpaw Hare Jan 19 '13 at 22:17
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closed as not a real question by Kris, Kristina Lopez, RegDwigнt Jan 19 '13 at 11:23

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4 Answers

Curved brackets, or parentheses (like these), are used to set off different kinds of interruption to a sentence. Square brackets [like these] are used in a quotation when the words contained in them are not part of the quotation, but are necessary for the sense. Curly brackets, or braces {like these}, are rarely used in normal writing. They are mostly reserved for specialised texts.

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  • Brackets — [] — are used to enclose "meta information" regarding text — text that is used to explain other text from an outside point of view. As an example, brackets can be used to give context to a direct quote by replacing or adding words that were not actually said in that exact manner, yet help to understand the meaning.

    I don't know, [the crazy monkey] bothers me.

    The term sic is generally put in brackets, expressing an intentionally recreated mistake in a quote.

    I ordered my sandwich with cheeze [sic] and ham.

    It can also be used to show citations, as done on Wikipedia.

    Southpaw Hare is an awesome dude. [15]

  • Parentheses — () — are used mainly for asides or secondary thoughts that step away from a main thought before returning.

    There is a big difference between rabbits and hares (although you can use 'bunny' to refer to either of them).

  • Braces — {} — don't have any mainstream use in ordinary English — they are used in various technical fields for special expressions.

Most information from Wikipedia's page on Brackets.

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The terminology here is American, but the rules are fairly universal. –  TimLymington Jan 19 '13 at 11:20
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Perhaps it would be better to address parentheses as parts of sentences before discussing the punctuation involved; it can be confusing that the word has such a dual role. At http://josecarilloforum.com/forum/index.php?topic=459.msg1503#msg1503 is:

... information ... set off by the punctuation marks — whether by commas, dashes, or parentheses — is called a parenthetical [or simply parenthesis, EA], and its distinguishing characteristic is that the sentence remains grammatically and semantically correct even without it. A parenthetical is basically added information; however, it isn’t necessarily optional or semantically expendable. It may be needed to put the statement in a desired context, to establish the logic of the sentence, or to convey a particular tone or mood for the statement. In fact, the punctuation chosen for a parenthetical largely determines its optionality or importance to the statement.

Carillo goes on to discuss the choice of commas, dashes, or parentheses to set off parentheses (parentheticals). He may be over-analytical; it is true, however, that commas signal the least abrupt interruption to the matrix sentence and dashes the most abrupt.

Mark Nichol (at http://www.dailywritingtips.com/8-types-of-parenthetical-phrases/ ) discusses different uses of parentheticals, though parentheses would not be preferred over commas say for all types in all situations.

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I believe that the general rule of thumb is to always use parentheses (round) and use brackets (square) for special situations or to avoid ugly parenthetical nesting. Braces (curly) are hardly ever, if at all, used.

Their usage is covered in this guide on ODO:

Parentheses are mainly used to separate off information that isn’t essential to the meaning of the rest of the sentence. If you removed the material within the parentheses, the sentence would still make perfectly good sense.

They can also be used to enclose a comment by the person writing ...

Brackets (also called square brackets) are mainly used to enclose words added by someone other than the original writer or speaker, typically in order to clarify the situation ...

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Having square brackets on the inside is certainly uglier than having nested parens. –  tchrist Jan 19 '13 at 22:33
    
@tchrist I do believe that it's the style in Chicago :) –  coleopterist Jan 20 '13 at 5:32
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