Except for the beard, which is haram to shave (obligatory precaution), not only is it permissible to remove the hairs of the body such as the armpits, but it is mustahabb in Islam, and has been prescribed in many hadiths, but isn't wajib either.
 Tawdihul-Masa’el (annotated by Imam Khomeini), vol. 2, pg. 835, issue 40: “Shaving the beard with a blade or machine (voluntarily) is haram according to obligatory precaution.
 Al-Hoseini Al-Jorjani, Al-Seyyid Al-Amir Abul-Fat’h, Tafsir Shahi, vol. 1, pg. 93, quoted by the Jame’e Fiqhe Ahle Bayt software. “It is an Islamic tradition to apply depilatory every fifteen days or forty days….”
 Al-Kuleini, Al-Kafi, vol. 6, pg. 505; Tahrirul-Ahkam Al-Shar’iyyah ala Madhabil-Imamiyyah, vol. 1, pg. 8 and on.