Globally override key binding in Emacs

How can I set a key binding that globally overrides and takes precedence over all other bindings for that key? I want to override all major/minor mode maps and make sure my binding is always in effect.

This of course doesn't work:

(global-set-key "\C-i" 'some-function)

It works in text-mode, but when I use lisp-mode, C-i is rebound to lisp-indent-line.

I can go through and override this binding in lisp-mode and in every other mode individually, but there must be an easier way. Every time I install a new mode for a new file type, I'd have to go back and check to make sure that all of my key bindings aren't being overridden by the new mode.

I want to do this because I want to emulate bindings I've already learned and ingrained from other editors.

I use a minor mode for all my "override" key bindings:

(defvar my-keys-minor-mode-map
  (let ((map (make-sparse-keymap)))
    (define-key map (kbd "C-i") 'some-function)
    map)
  "my-keys-minor-mode keymap.")

(define-minor-mode my-keys-minor-mode
  "A minor mode so that my key settings override annoying major modes."
  :init-value t
  :lighter " my-keys")

(my-keys-minor-mode 1)

This has the added benefit of being able to turn off all my modifications in one fell swoop (just disable the minor mode) in case someone else is driving the keyboard or if I need to see what a default key binding does.

Note that you may need to turn this off in the minibuffer:

(defun my-minibuffer-setup-hook ()
  (my-keys-minor-mode 0))

(add-hook 'minibuffer-setup-hook 'my-minibuffer-setup-hook)

As an addition to scottfrazer's answer, I've written the following so that my keybindings retain precedence, even if subsequently-loaded libraries bring in new keymaps of their own.

Because keymaps can be generated at compile time, load seemed like the best place to do this.

(add-hook 'after-load-functions 'my-keys-have-priority)

(defun my-keys-have-priority (_file)
  "Try to ensure that my keybindings retain priority over other minor modes.

Called via the `after-load-functions' special hook."
  (unless (eq (caar minor-mode-map-alist) 'my-keys-minor-mode)
    (let ((mykeys (assq 'my-keys-minor-mode minor-mode-map-alist)))
      (assq-delete-all 'my-keys-minor-mode minor-mode-map-alist)
      (add-to-list 'minor-mode-map-alist mykeys))))

Install use-package, eval and you're done:

(require 'bind-key)
(bind-key* "C-i" 'some-function)

I found this question while searching for "emacs undefine org mode keybindings", because I wanted to unbind the existing C-c C-b behavior to allow my global map to bury-buffer to work in an org buffer.

This ended up being the simplest solution for me:

(add-hook 'org-mode-hook
      (lambda ()
        (local-unset-key (kbd "C-c C-b"))))