ANSWER
The short answer: The water level will fall.
The longer explanation: The anchor, being heavier (denser) than water, will sink to the bottom once it is dropped into the lake. You probably remember from your high-school physics that floating objects displace an amount of water equal in weight to the weight of the object. However, this is only true of floating objects. Since the anchor does not float it will only displace an amount of water equal to the size (volume) of the anchor. On the other hand, when the anchor is in the boat the anchor and boat together are floating. In that case the water displaced by the anchor portion of the anchor/boat combination is equal to the amount of water whose weight equals the weight of the anchor.
Let's assume, for the sake of argument, that the anchor weighs 50 pounds. Thus the anchor in the boat is displacing 50 pounds worth of water. Now the anchor at the bottom of the lake is displacing an amount of water only equal to the size of the anchor, and since the anchor is heavier (denser) than water, the amount of water it displaces must be less than 50 pounds. Thus, since the anchor is displacing less water at the bottom of the lake than it was when it was floating in the boat, the overall affect of dropping anchor will cause the water level of the lake to fall.
Just to make certain that our conclusion was sound, the scientists here at The Manbottle Library conducted extensive physical testing during halftime of the NFC Championship game. (Go Bucs!) Our results were as expected, despite any additional measurement error introduced by the consumption of alcohol on the part of the ordinarily very sober scientists. Or something like that. (While the results of the anchor experiment made sense, our scientists are still somewhat puzzled about how the Bucs actually made it to the Superbowl. This will require additional research.)
(Honorable mentions go to Brett Dougherty for noting that the effect of evaporation of water droplets created by the splash of the anchor would slightly reduce the level of the lake. To Robert Walker for questioning the effect of water being absorbed by the rope to which the anchor was attached. To Allan Christensen for noting that most lakes in Massachusetts would be frozen over at this time of year, causing the level to remain the same as the anchor sat on the ice after being tossed from the boat. To Bob Milligan for actually attempting to repeat the experiment, although with not quite enough precision to arrive at the correct answer. And to Steve Shuba for a clever variation of the problem involving a home-made anchor made from a styrofoam cooler, a handful of Craftsman tools, and some duct tape. Don't ask.)
A more thorough explanation of the question and its solution can be found here...
http://www.amherst.edu/physicsqanda/Rowboat.htm
WHO GOT IT RIGHT: John Trotter, JP Weigt, Craig Buchanan, and Steve Shuba.
