It varies largely by region and by what parts you're looking for. If all you're talking about is getting a particular cut of steak, that shouldn't be a problem for most places although I don't call that butchering. If you want something a bit more exotic like pig liver, caul fat, etc. your options quickly become limited. Some places will let you special order less common parts (i.e. sweetbreads, kidney) if you meet minimum increments, and some cuts (tripe, tongue, oxtail, etc.) you can more easily find at an ethnic market however you really need to know where to look. However to get other parts (i.e. a full hog's head, pork liver, etc.) you need to find a real butcher and those are becoming increasingly less common. This is partially dicated by health code requirements that need certain parts (i.e. fresh liver) to meet certain guidelines that can't be done unless you cut the whole animal there.
In the SF Bay Are where I live we still have some good local butchers (The Fatted Calf, The Local Butcher Shop, Golden Gate Meat Co., etc.) however you pretty much have to know where to look and be willing to drive. For example, in the East Bay I only know of one store that does full butchering (Lunardi's in Walnut Creek) and even local butcher shops like Lawrences Meat in Alamo or Main St. Meat & Fish Market in Pleasanton don't get the whole animal.
I have limited experience in Brooklyn, New York, and I found it a but easier to find local butchers over there. However that may well be changing.