There are many cocktails made with all sorts of exotic names. But in the UK (and maybe elsewhere for all I know) there are beer cocktails as well. Somre of those I remember are:

Black Velvet: Guinness and champagne
Mother-in-law: Old and bitter
Grandmother: Old and mild
Snake bite: Lager and cider
Black and Tan: Guinness and bitter

Snake bite is one of those drinks that has the (quite false) reputation of making its users far more drunk than would be the case were they to be drinking either one of the drinks on its own. This simple truth is that cider, especially scrumpy, can be very strong at between 8% and 10%. Premium lagers, too, can be strong and thus the mixture is a fairly lethal one- but it's the alcohol, not the mixing, that does the trick.

Anyone know any more beer cocktail names?

A French 88 is Guinness and champagne with a shot of cognac in it. Dates from the Western front in the Great War. Deadly.

A sneaky Pete: red wine and beer. Never had it, and it sounds disgusting.

Don't know if it qualifies as a cocktail -- probably not. But on a really really hot day I love a good chewy stout with French vanilla ice cream. Beer Floats! Yum...

I'd never heard of theses, so I did a bit of googling. I found beer cocktails here and here, and I'm sure there are more, but I couldn't handle reading more. The idea of the Michelada, with soy, Tabasco and Worcestershire in the beer was enough for me.

The Yardhouse, a new bar near where we live, has about 110 beers on tap. There was one that was a mixture, but I just don't recall the name. I know that it was Guinness mixed with something, but I don't know what. Maybe it was Richard's "Black and Tan," but I surely don't recall the other part being a "bitter."

Generally, though, I don't think beer cocktails are seen much in the Chicago area.

Boilermaker: Shot of whiskey and a beer
Depth charge: Shot of whiskey dropped into a beer (fun!)
Shandy: beer and lemonade
Shandygaff: strong beer and ginger beer
Red Eye: beer and tomato juice

I ordered a shandygaff at the Edinburgh Castle pub in San Francisco once, but I think I got beer and lemonade.

As I understood it, Shandy is simply an abbreviation for Shandygaff. And a Shandy is beer (usually bitter beer) and lemonade.

When ginger-beer is used it's a ginger-beer shandy; when lager is used it's a lager shandy.

Shandy is a very nice drink in the hot weather (much better than chemical lager).

The Boilermaker is a shot of whiskey with a mug of beer. Sometimes drunk mixed; sometimes the whiskey first with the beer as a chaser.