() : round brackets(in British English) and  'parentheses' in (American English)
{} : curly brackets(in British English) and 'braces' in (American English)
[] : square brackets(in British English) and  'brackets' in (American English)
<> : angle brackets(in British English) and 'chevrons' in (American English)  

Note : its up to you which language you would like to speak and pronounce. As I am an Indian so I would like to speak British style as our education system prefer this.

Usage:

Round brackets(Parentheses) are always used in pairs ().

Curly brackets(Braces) are used to group statements and declarations.

Square brackets(Brackets) are used primarily for array indexing. But they are also used to denote general tuples, sets and other structures depending on the language. just as in mathematics. There may be several other uses as well.