Does drinking beer make you stupid?

The short answer is "yes".  Beer and other alcohol have negative long-term 
effects which include killing brain cells, causing memory deficits, and 
impairing verbal and motor skills.  The following article describes the long-
term effects of alcohol consumption:

http://www.priorityonevitamins.com/health-nutrition/Alcohol.html

One relevant section of this page is titled "Do you know how BEER affects your 
body?"  The section includes the following text:

"And, in the brain, beer causes the destruction of brain cells which are unable 
to be regenerated or regrown. In fact, medical professors and medical students 
know that a drinker’s brain is almost worthless I teaching anatomy. Such a 
brain is usually saturated with watery fluid, and the nervous system has wasted 
away."

So, beer is definitely harmful to your mental abilities in the long run.  You 
probably already know about the short-term effects of beer, which include 
impaired judgement, motor skills, and verbal abilities.  These short term 
effects could probably be described as making you stupid too.  Here's another 
article from Dr.Koop.com titled "Drink Much?" that discusses the effects of 
alcohol:

http://www.drkoop.com/news/stories/feb/drunk.html

Some search terms I used to find this information:
alcohol effect human brain
effects of drinking beer

I hope this answers your question.  Thanks for using Google!

OK, thanks for the references, but I'd also like to find some information about 
the effects of more moderated consumption.

A search on the positive effects of beer consumption turned up a whole bunch of 
websites saying:"moderate drinking reduces the risk of heart and circulatory 
disease". 
On http://www.bierengezondheid.com/index_eng.jsp?Page=Dos92&Doc=matig they try 
to summarize how this positive effect can be explained.
But they also state that more scientific research is required. 

I suggest that you just visit the excellent Beer & Health website 
http://www.beerandhealth.com/ , and don't forget to take a look at the links 
under the header 'scientific research' in the left column.

Scientific medical research demonstrates that the moderate consumption
of alcohol (beer, wine and/or distilled spirits) is associated with
better health and greater longevity than is abstaining or abusing
alcohol. See the "Alcohol and Health" page at
www.alcoholinformation.org