- Reflexive and emphatic form of them when them is used as a non-gender-specific singular pronoun (singular they).
- Someone has hurt themself.
- Anyone who wants a car like mine can buy one themself.
- 2009 January 8, Samantha Maiden, “Hoaxer, out yourself: 'Demidenko'”, The Australian:
- THE author who masqueraded as Helen Demidenko yesterday urged the hoaxer who deceived the respected right-wing journal Quadrant to unmask themself.
- themselves in some dialects
- thonself obsolete
- xirself, eirself etc. (see Gender-neutral pronouns)
Usage notes 
While proscribed by many, this word has been in common use for hundreds of years. The issue stems from the use of they as a gender-neutral third-person pronoun, also considered non-standard. More information can be found at the usage notes on that page.
Although many alternatives exist, most of them are considered unacceptable in most contexts, so care should be taken in deciding which option is likely to be most acceptable for your audience.
- Using himself as gender neutral is often considered politically incorrect
- Using herself as gender neutral can sound forcefully politically correct.
- Using themselves in its singular meaning is also considered non-standard.
- Using some form of alternative syntax (him/herself, him(her)self) can be cumbersome.
- Using a constructed word (xyrself, eirself etc. — see Gender-neutral pronouns) can sound forcefully politically correct and run the risk of not being understood.
That being said, one should understand one's audience before deciding which form to use.