It is recommended to trim/shave/pluck under your arms, in your pubic region, and your moustache area. Removing other unwanted body hair like on the chest, back, and legs is allowed, and is often done for sports or for style.
If an area of your body may be trimmed, shaved, or plucked, then it is allowed to remove it permanently as well, as long as there are no harmful side effects. This is similar to constantly plucking it.
What the Scholars Said
A group of scholars stated, “Shaving the hair of the chest and back is contrary to proper manners (adab).” (Al-Fataawaa Al-Hindiyyah, 5:358)
It has been argued that there must be some wisdom behind why Allah created hair on certain parts of the body, so it should not be removed permanently. However, not all people have hair in the same areas and removing it, despite Allah creating it, is similar to circumcision where some of the foreskin is removed for the purpose of greater cleanliness, except that permanent hair removal is more for convenience or beautification.
Shaykh Mustafa Umar