When did women in Europe begin shaving their legs and armpits? Would all medieval women be considered "hairy" by today's standards?

This is a tough one. The Internet loves women's hygiene badhistory almost as much as it loves food badhistory, and what to my knowledge is the major scholarly article on body hair in the Middle Ages takes nearly all its evidence about women from the sixteenth century.

That said, for the later Middle Ages, removal of women's body hair--especially pubic hair--is amply discussed in two types of sources: medical texts and satire. That probably means some if not many Western women, or at least middle/upper class women, sought to remove body hair. It definitely suggests there was some discomfort in talking about the idea.

Medieval art and literature make it clear that body hair was primarily a sexual symbol, associated as it biologically is with puberty. For men, this was primarily a positive thing. (After all, virility comes from vir, manly-man). Although male beauty was strongly tied to youth, what we might call 'manliness' was less so. For women, things were more complicated. Public hair/body hair did continue to represent unbridled sexuality.

But--so did its removal. Erasmus' Moriae Encomium (Praise of Folly) counts among its fools old women who prepare for their sexual exploits by tweezing their pubic hairs. The implication in that paragraph, particularly as paired with the immediately preceding enumeration of the follies of randy old men, is that they take this action to try to recapture their youthful, sexual days. Erasmus is of course writing satire, as are his contemporaries who ridicule prostitutes for trimming or completely removing The Hair Down There. That makes it hard to say how widespread a practice depilation actually was, on its own. But the common strand among the texts points to a deeply entrenched cultural value on pubic hair/pubic hair removal.

Medical texts from the later Middle Ages offer another set of evidence for the practice of hair removal, although again, the connection between medical texts and actual practice is...frequently contentious. An extra wrinkle here is the importance of Greek and Arabic influence over the later Latin (and through that, the western vernaculars) medical tradition. Both ancient Greece and the contemporary Islamic world practiced depilation, so references in western texts could be either artifacts of that or attempting to push those mores on the west.

One really interesting piece of evidence is one of the texts in the Trotula, De ornatu mulierum (On Women's Adornment). The Trotula is a group of 12th century texts that medieval writers attributed to a female medical practitioner and author named Trota; Monica Green argues persuasively that "Trota" or another woman did indeed write at least some of the texts and that her influence can be detected behind them all. De ornatu mulierum discusses depilation in quite a bit of depth--methods, the influence of "Saracen women" on the western practice, and so forth. It's important to note that depilation is THE FIRST subject discussed by this text. Straight off:

In order that a woman might become very soft and smooth and without hairs from her head down...

Most of the methods are a non-wax version of waxing (quicklime is a common ingredient). And then, because the Trotula is awesome, it goes on to discuss the medieval equivalent of how to heal razor burn. (...Egg whites. No, for real.)

Oh, and after you wax, you should take a nap. :)

Later medical authors reiterate similar depilatory methods. A subsequent text that claims to be "from Trota" (but is clearly not) includes them alongside what we might see as more "medical" cures and information. And Henri de Mondeville, the early 14th century French surgeon, has quite a lot to say in his Surgery about women removing body hair! He reports that women like to remove all the hair below their heads. While he is quick to say he disapproves, he is equally sure that medical practitioners must be involved or must at least give advice in order that they do it as safely as possible. Much like the humor/satire writers discussed above, Henri explicitly connects hair removal with the restoration of youth and an attempt to cast a false air of chastity.

Which would only be a factor if the woman were going out to have sex, of course.

Edit: You probably all want to read the article I mentioned at the beginning (Penny Jolly's "Pubics and Privates: Body Hair in Medieval Art"), so, here's what you can get of it from the Google Books preview. It's not medieval, but don't miss the discussion about Pierre de Brantome's Les dames galantes starting on p. 192 for sheer entertainment value.