Emacs Init: Auto Insert Closing Bracket

electric-pair-mode

Toggle auto insert of closing bracket. When on, typing any left bracket automatically insert the right matching bracket.
New in emacs 24. [see Emacs 24 (Released 2012-06)]

put this in your Emacs Init File:

;; auto close bracket insertion. New in emacs 24
(electric-pair-mode 1)

Exactly which brackets are paired depends on the buffer's Syntax Table, which usually is set by current Major Mode .

If you always want certain brackets be inserted in pairs, you can customize the variable electric-pair-pairs. Its value should be a Association List.

;; make electric-pair-mode work on more brackets
(setq electric-pair-pairs
      '(
        (?\" . ?\")
        (?\{ . ?\})))

[see Unicode: Brackets, Quotes «»「」【】《》]