(customize-variable (quote tab-stop-list))

or add tab-stop-list entry to custom-set-variables in .emacs file:

(custom-set-variables
  ;; custom-set-variables was added by Custom.
  ;; If you edit it by hand, you could mess it up, so be careful.
  ;; Your init file should contain only one such instance.
  ;; If there is more than one, they won't work right.
 '(tab-stop-list (quote (4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104 108 112 116 120))))

Do not confuse variable tab-width with variable tab-stop-list. The former is used for the display of literal TAB characters. The latter controls what characters are inserted when you press the TAB character in certain modes.

-- GNU Emacs Manual

(customize-variable (quote tab-stop-list))

or add tab-stop-list entry to custom-set-variables in .emacs file:

(custom-set-variables
  ;; custom-set-variables was added by Custom.
  ;; If you edit it by hand, you could mess it up, so be careful.
  ;; Your init file should contain only one such instance.
  ;; If there is more than one, they won't work right.
 '(tab-stop-list (quote (4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104 108 112 116 120))))

Another way to edit the tab behavior is with with M-x edit-tab-stops.

See the GNU Emacs Manual on Tab Stops for more information on edit-tab-stops.