They anchor right into the reef.  In some areas you can see long gouges where the anchor has ripped right through the rock.
However, the new thing to do is that many popular diving places have bouys set up tied to the bottom.  Then boats come and they all tether to the bouys.... thus eliminating the need to anchor.

Here is another story.  It is very common for boats to drop off divers and simply drift.  When the diver returns he swims to wherever the boat is.  It is also common for on small boats that when divers surface they blow a horn and the boat comes to pick them up.  I once surfaced, couldn't see the boat, and couldn't see land.  I told my diver partner "well I guess I'll blow the horn, I hope they come for us".  It took a couple minutes but the boat did come pick us back up.  I was quite relieved to say the least.

Adam

Or the boat trys to follow the bubbles and drift along with the divers.

Where's adam, or diverdan, when you need him?

LOL...........

Kinda funny that this (northern reef) topic popped up here.  In passing, Adam and I had a similar discussion over some pizza a couple weeks back, only I was under the impression that it was off the coast of Alabama, but I couldn't remember the name/location/ect.  Well, the guy I know (catalyst salesman from Houston) who has dived there just made his monthly visit.  It turns out the place is called The Flower Gardens.  They are about 100 miles off the Texas/Louisiana coast and are according to NOAA, the most northern coral reefs in the USA.  Here's NOAAs website for the area:  http://www.sanctuaries.nos.noaa.gov/oms/omsflower/omsflower. html

Carl, is that the area that you heard about in Corpus Cristi?  The recent history of the Flower Gardens is kinda interesting.  They were only "recently" discovered and were kept a "secret" until Shell Oil Exploration started drilling in the area.  The mud from the drilling operation started to kill the reef.  A concerted effort by gulf coast divers and environmentalist got the dilling stopped and the area protected from future drilling.

Carl wrote: Well Mr. Adam, what is the northern most reef then? Is it the northern most in the U.S.?

I hate to say what the northern most is because I'm not actually sure on that.  The reef systems around Japan reach around 40 latitude (I can't find a degree symbol on my keyboard gosh dang it).  Off the top of my head that is what I would guess.  As for the US, once again debatable but I do consider East Florida up to Jacksonville to be a reef.  I don't consider Georgia and the Carolinas to be reefs.  Side note- the islands in the Sargasso Sea are reefs and they are further north of the Carolinas and just off the coast. 

Adam