The honor of what is probably one of the weirdest law in any western country ever goes to backward hillbilly Icelandic politicians who for decades banned the sale and consumption of beer in the whole country. Hard liquor was fine and dandy though.
These rather stupid politicians; for whom bans beer and not hard alcohol in an attempt to limit drinking in one country, have thankfully gone away and since 1989 Iceland has mostly been a real place with real beer.
Well, strike the last sentence for we did not really have decent beer at first. Naturally the market flooded right away with superficial light stuff and it has really gone downhill from there up until just a couple of years ago.
What you get at 98 per cent of bars and restaurants across the country today are rather horrible lightweight local beers like Viking, Polar and Gull all of which are produced by the largest drinks companies in Iceland. These also distribute average stuff from abroad and you can be sure to get you fill of Carlsberg or Tuborg most places you go.
For the real stuff you need to keep your eyes open or bluntly ask. Some brewers making a splash for quality stuff are Olvisholt brewery with Skjalfta, Lava and Mori beers. Also refreshingly tasteful are beers lika Kaldi and some like Borg Brio very much. Also a favorite for many is Einstok beer.
Specialty beers are sadly not widely sold but often you can find one or two brands at most better hotels and bars in bottles. In Reykjavik, the Micro bar, is your best bet. This small place is right by Austurvollur square. Also Kaldi bar in Oldugotu near Laugavegur shopping street. Elsewhere it is just luck which bar stocks a variety of beers.
Also make sure you´ll stop a the wine monopoly store where most specialty beers are available at most times. Rough bar price for a pint of lager would normally be around 900 – 2000 ISK depenging on time to day. Some bars offer half-price between 16 and 19 on weekdays.