How to insert tab character in Text mode?

C-q <tab>

C-q insert the next character as a raw character

In addition to answer given: Check value of indent-tabs-mode, customize it if needed. Several hooks use it's value doing translations TAB-Blank.

If you want TAB key to insert a tab character, add this to your ~/.emacs

(global-set-key (kbd "TAB") 'self-insert-command);

More helpful info on emacs + TAB : https://web.archive.org/web/20160312104535/http://vserver1.cscs.lsa.umich.edu/~rlr/Misc/emacs_tabs.htm