As a Canuck (and, if it matters, largely a Torontonian) I’ve always “took” showers, but “had” baths. On the other hand I’ve also heard “have” the old alliterative “Have a shit, shower and shave” as well, but only ever in that context.
Okay, I have been lurking here long enough, and now that a good opportunity to join this bath of dopers has revealed itself, I shall plung in. So look out, here I come!
This post seems to already have taken several directions, depending on where the shower is taken, so I’ll divert the attention to taking the shower elsewhere, because from where I come from, we have a saying when you actually skip the shower and just cover up with some perfume, we say that you took/had an “English shower”. Dont ask why the english are held by the scruff in this saying, no harm intended, but thats just the way the saying goes over here.
Over here, if you wash just your armpits and face, it’s called a Marine bath. Jarheads, you see, are a scummy lot. 
It seems to have a long history, in which The Vikings in England even had a particular reputation of excessive cleanliness, due to their custom of bathing once a week
Well, today its Sunday, and I should start my weekly wash, better get out my earspoon too 
As in Brighton.
Native Bostonian, current southern californian, well-traveled around the country.
Not until I opened this thread have I ever once in my life heard the term “have a shower”.
Here in Edmonton, the have/take phrasing is completely interchangeable. I’ll have a shower or take one, have a bath or take one. The word that comes out is almost random.
That’s good, for I don’t think you would be allowed to take anything from the Diefenbunker.
My favourite archaic Englishism is “to draw a bath” (one usually gets the butler to do this for one).
My dad used to ask me to draw him a cup of coffee. He stopped after I presented him with a piece of paper upon which I drew a cup of coffee.
HA!
Knew they had one somewhere!
Completely OT (sorry), but… the second article (from Columbia Uni. Press) is, well, strange. We go right from the scandinavian neolitic period to the so-called viking age and from there into a detailed account of viking ships. Really strange priorities by the author of that article :dubious: 
I believe that we in the Pacific Northwest are fairly unique in that we neither have nor take showers but fingerbang them.
Slight hyjack: When visiting Europe some years back, hotels in multiple countries had bathtubs with showerheads positioned on the long side of the tub, not at one end. And the shower curtains were only wide enough to go around half of the tub. Those were the most cautious showers I had ever taken. Is this typical? If so, how does one shower without getting water all over the floor?
And in true “pass the abuse on to some other nation” style, in England that’s known as a “Mexican shower”…
I stayed in a hotel in Austria that had a shower/tub sticking out into the middle of a fairly large bathroom that had no curtain whatsoever. The CW passed on to me at the time was that European hotels only installed showers to appeal to American travellers (European travellers apparently showering infrequently enough that they wouldn’t feel the need to have one in the hotel), and the hoteliers weren’t too clear on the concept. That may have been utter horseshit, obviously. It hasn’t occurred to me again until now, so I never bothered to check into it.
In some hotels, you get a small bathroom, with a shower but no shower curtain, and there’s a drain on the floor. You just treat it as a wet room and try to hang your towel somewhere that avoids the spray…
But honestly, in England we’re quite civilised now. In any decent hotel, proper showers are very much the norm, with those giant “rainfall” showerheads increasingly popular. Some places you’ll even find soap. 
But is the toilet paper any better?

I’m sort of serious. When I was flying in and out of Blackbush in the 50’s, we’d hole up in the same dreary, strait-laced (no chicks in the room) London hotel, whose TP was as soft and absorbent as tree bark.
BTW that was my only complaint - ever - in London. And I’m still very fond of the English.
Although I don’t remember specifically, it would seem that hotel had showers. None of the crew ever remarked about it.
Ah, the old shiny TP, eh? That seems to be just about extinct now. I remember we used to have it at school back in the 1980s, but I haven’t seen any of that stuff for at least 10 years now.
BTW, interested to hear you flew from Blackbushe. I live less than a mile from that airfield. It’s a lot smaller than in its heyday, but still used by lots of private planes (including trainee pilots, who occasionally make the local headlines by landing on roads, roofs of buildings, other aircraft, and other inappropriate locations).