ANSI Coloring in Compilation Mode

There's already a function for applying color to comint buffers. You simply need to enable it on compilation buffers:

(require 'ansi-color)
(defun colorize-compilation-buffer ()
  (toggle-read-only)
  (ansi-color-apply-on-region compilation-filter-start (point))
  (toggle-read-only))
(add-hook 'compilation-filter-hook 'colorize-compilation-buffer)

Color writing programs should check the TERM environment variable and the terminfo database to check if the terminal supports color. In practice, a lot of programs ignore this and rely on a user setting. Emacs will set the compilation terminal type to dumb by default but this can be overriden by setting the compilation-environment variable.

Update: Note that in Emacs 24.5 the two calls to (toggle-read-only) in the code above are not needed.

My optimized solution which don't pollute M-x grep (only for M-x compile):

(ignore-errors
  (require 'ansi-color)
  (defun my-colorize-compilation-buffer ()
    (when (eq major-mode 'compilation-mode)
      (ansi-color-apply-on-region compilation-filter-start (point-max))))
  (add-hook 'compilation-filter-hook 'my-colorize-compilation-buffer))