In the UK, most women shave their armpits.
Anyway, since when did "armpit" become an unmentionable word - it's perfectly descriptive. "Axilla" is a bit clinical but "underarms" sounds stupid to me. It's like calling the neck the "underhead"
It is my experience that some women in central Europe don't shave their armpits. The only woman I know who doesn't shave (or wax, presumably) that part of their anatomy is a (very "out") lesbian in New York!
As for health, I can't see that it's an advantage to shave - skin irritation can result and it has been shown that deodorants, together with shaving, can increase the likelihood of breast cancer.
Smell may be another thing - I can understand that pheromones linger on hair longer than on shaven skin...but that's about cosmetic choices, I would suggest.
For the record, unless it's excessive, I don't find women sporting hair under their arms unattractive. Hairy legs or lop lips are another story...ugh!