Speaking for the Ancient Greeks here: we know that people shaved quite a lot. Possibly their whole bodies. The main tool for this was the razor; sharp knives were common, everyday items. But they also used other methods including epilating and singeing hairs off with fire.

The reason we know about this is that a great deal of comedy from the Classical period revolves around cross-dressing (women as men and vice versa). The process presented the opportunity for many jokes about body hair. We get the women's perspective in Aristophanes' Assemblywomen, in which citizen women dress up as men in order to take over the Assembly and pass a decree to change the constitution of Athens to a sort of proto-communism. At the start of the play the women discuss what they had to do to achieve this:

First woman: Firstly, as agreed, I have let the hair under my armpits grow thicker than a bush; furthermore, while my husband was at the Assembly, I rubbed myself from head to foot with oil and then stood the whole day long in the sun.

Second Woman: So did I. I began by throwing away my razor, so that I might get quite hairy, and no longer look like a woman.

Praxagora: Did you bring the beards that we had all to get ourselves for the Assembly?

These lines imply that a razor was a typical possession for an Athenian woman, and that it was normal for these women to keep various body parts clean-shaven, including their armpits. As Aristophanes says, to stop shaving and let body hair grow out is to "no longer look like a woman".

The comedian explores the reverse in his comedy Women of the Thesmophoria, in which the male main character Mnesilochos tries to infiltrate a women-only religious festival in order to prevent them from plotting against him. To pass as a woman, Mnesilochos must dress as one, but he must also get rid of his body hair. To get advice on the best look, he turns to the poet Agathon, who is characterised here as an effeminate pretty boy who is willing to play the submissive partner to other men. Part of his characterisation is the fact that he dresses nicely, smells of perfume, and is clean shaven. As Agathon is made to say, "it is bad taste for a poet to be coarse and hairy" (159-160); the playwright Euripides (another character in this comedy) remarks that Agathon always has a razor within reach to maintain his handsome appearance (217-218). What does he want with the razor?

Euripides: To shave off this beard of yours, and to remove all your other hair as well.

Mnesilochos yelps and whines his way through having his face shaven by Euripides. But when he thinks he is finally through it, the real ordeal begins:

Euripides: Stand up; I am now going to remove your hair. Bend down.

Mnesilochos: Alas! alas! they are going to grill me like a pig.

Euripides: Come now, a torch or a lamp! Bend down and watch out for the tender end of your tool!

Mnesilochos: Aye, aye! but I'm on fire! oh! oh! Water, water, neighbour, my asshole is on fire!

Euripides: Keep up your courage!

The implication of a scene like this is that in order to look like a woman, a Greek man would have to shave off not just his beard, but also the hair on various other body parts, including (probably) his legs and his butt. The use of a lit oil lamp for the purpose would make sure that even hairs hard to reach by razor would be removed.

There's a lot of cruel comedy in this scene at the expense of a rather ridiculous and unsympathetic main character. But there's also some sensitivity to the routine suffering of women. Mnesilochos deserves what he gets, but no man in the audience was likely to volunteer for the same treatment. Shaving was something for other people to do in order to be attractive to men - something that was expected of women and less overtly masculine men, but not something that most men were likely to inflict on themselves. Adult Athenian men generally had beards, shaved no part of their bodies, and looked down on men who retained a smooth chin beyond boyhood. But then, they were also attracted to smooth skin, and didn't much care whether it was found on women, boys or adult men. Each of these probably faced pressure to remove all body hair by any means necessary.