So I checked Wiki, and it says that “cask” beer was typically stored in the cellar of the pub and pumped up by hand.
Why is it only done in the UK? Why don’t American pubs, for instance, do this? I’ve heard people say that the whole “added CO2 to make it squirt out the tap” thing spoils the taste, and I have to say that the best beer I’ve ever had has been in English pubs, pulled up from the basement by hand–but maybe that’s a) because of the ambiance and b) because it’s better beer.
Some American pubs do…but relatively few. There’s a pub here in Rice Village that does it, and only for locally brewed ales. It’s quite a treat; it imparts quite a different taste and mouthfeel to the beer.
The Gingerman, right? That was my regular hangout when I was a Houston dweller back about five years ago. 
Yes, very good! 
My local bar also pulls one of their beers. It’s whatever is currently available from Yards Brewery. Which is currently the Philadelphia Pale Ale. Quite tasty.
There’s a Gingerman in Austin, too. Is it a chain?
a) yes
b) yes
Cask beers can be found at any number of better establishments around the country. Even chains like BJ’s Restaurant and Brewery will have cask ale whenever the brewers get the time to make some.
Of sorts. There are three or four locations, I think.
There are bars that serve cask ales in the DC area, too - like The Brickskeller and RFD. The Green Leafe Cafe in Williamsburg, VA will tap a cask every Thursday.
When I was last in an Alcatraz Brewing Co. brewpub, they had one ale that was pulled. The barmaid tried to talk me out of it because it wasn’t fizzy.