There are fatwas for pretty much everything a Muslim does with his/her body (or his life) including what hair you can or cannot remove.
Different clerics and schools of thought vary slightly on certain areas of the body, and the method of removal, except for a few things that are non-negotiable:
the eyebrows - not pluckable by either men or women, even if you look like Frida Kahlo.
the pubic area and armpits- must be shaved by both men and women, and you cannot go longer than 40 days without shaving those pubic hairs. [Who would have thought!]
The following Fatwa Show video sketch pokes fun at this specific fatwa, referencing the actual fatwa by Saudi cleric Sheikh Mohammed Bin Saleh al-Othaimeen.
Other fatwa sources on body hair removal: