What's with Kamesennin's nose bleeds?

[Blade]

On a side (and partially related note), I've always liked Eiichiro Oda's pastiche on the trope in One Piece with Sanji, whereby his nosebleeds are taken to extreme and increasingly ridiculous lengths.

This culminates on Fishman Island, where surrounded by such a large quantity of beautiful women, Sanji loses so much blood through his violent eruption-esque nosebleeds that his life is genuinely endangered and he requires a blood transfusion. The fact that the dramatic tone quickly veers from light-hearted comedy to a stern and bleak situation is a really interesting piece of satire, and quite well executed in that it doesn't break the suspension of disbelief - despite how thoroughly lurid and ridiculous it is on paper.

[SaiyaJedi]

And is falling on their heads like a facepalm or something?

It's called a "facefault", and happens in reaction to something absurd/idiotic/audacious/ridiculous. Like a physical version of Charlie Brown's "AUGH!"

[Kid Buu]

Is there some kind of cultural reason as to why Muten Roshi starts spewing blood from his nose every time he gets a glimpse at nudity? I'm surprised I haven't asked this sooner because I thought this was actually normal as a kid. But, seriously, it's really bizarre.

It's a visual shorthand for sexual excitement. It's used with both men and women, though more common with men, as it serves as a convenient euphemism for an erection.

Other shows have ladies having nosebleeds? Only one I've seen was on Sekirei, but didn't know others had women nosebleeding.

Sakura gets one in the Naruto manga - chapter 347.

[omegalucas]

Sakura gets one in the Naruto manga - chapter 347.

Konohamaru's male Sexy no Jutsu right?

[Kid Buu]

Yup! A shame he gave us Sasuke/Sai but not any proper female characters for the other version. *cough* Tsunade/Shizune please *cough*

[Adamant]

And is falling on their heads like a facepalm or something?

It's called a "facefault", and happens in reaction to something absurd/idiotic/audacious/ridiculous. Like a physical version of Charlie Brown's "AUGH!"

It's also an imported American trope, not an originally Japanese one. It's not really used much outside Japan nowadays, but check out some classic E.C. Segar Popeye strips or something, and you'll see it all over the place.