Are there any microbreweries in Iceland? If so, are any of them in Reykjavik?
What is the most distinct / unique beer from Iceland that one can get at the supermarket?
As of today (2016), there are several microbreweries operating in Iceland. The micro- and homebrewing scene has been budding nicely in the last few years, the latest player being Segull 67.
Other microbreweries are:
At the time of writing, this list is exhaustive for operational breweries. In addition, I know of three breweries which will be opening "any day now": Hún/Hann brugghús (in Reykjavík), Austri (in the eastern part of the country) and Hið austfirska bruggfélag (also in the eastern part of the country).
In addition to the breweries that sell nation-wide, there are a few who focus on their own premises.
Several bars pride themselves on selling Icelandic micro- and craft brews. These are:
Micro/Craft beer fans will also want to know of Mikkeller & Friends Reykjavík. Large tap selection there, but no focus on local produce.
Borg and Einstök taps can commonly be found interspersed with the common Egils and Víking taps. Steðji and Ölvisholt beers are only sporadically found on taps.
Many other bars (but definitely not all) have some ambition when it comes to craft beer availability without making a particular deal of it. Hlemmur Square, a hostel/bar near the main bus station, is usually particularly well stocked. But always, ask your bartender!
Off the top of my head, here are a few items I consider distinctive - or at least, I have not found anything quite like them abroad.
And always, keep an eye out for seasonal beers. The breweries usually allow themselves more creative freedom on those products. In 2014, we saw beers like the Einstök Arctic Berry Ale (beer flavored with Icelandic berries), Fenrir (an IPA smoked with sheep dung) and Hvalur (the whale beer mentioned earlier).
You won't buy Icelandic beers in the supermarket. The things that look like beers in those shelves are low-alcohol versions. To buy beers, you must go to one of the state-operated "Wine stores" (Vínbúð). Beware of their opening hours - they are never open after 20:00, on Sundays, or on holidays.
Source: Icelandic beer enthusiast.
Yes, there are craft breweries in Iceland. There aren't that many, but with a population of only 300,000 people that's to be expected. The main ones are Einstök, Borg, Gædingur, and Ölvisholt. There's also Stedji and Kaldi, but these are less interesting. I felt Gædingur was a bit variable on quality. Note that none of these produce extreme beers. They focus more on drinkability.
Only Borg is in Reykjavik. I don't know if you can visit the brewery.
You can't buy interesting beer in Icelandic supermarkets, because the alcohol limit is 2.25%. As far as I could tell, only 4 beers were available in supermarkets, all of them pale lagers. You have to go to Vinbudin. There's a branch in the Austurstræti in the city centre, but the one out in the Kringlan shopping center has a bigger selection.
Look for these bars in the Reykjavik city centre: Micro Bar, Cafe Laundromat, K-Bar, and 73. All of them on Austurstræti and Laugarvegur.
Edit: I forgot to say what's the most unique/distinct beer. I'd say Borg Fenrir, which they describe "tadreyktur IPA", meaning IPA smoked in the traditional Icelandic way. That is, it's smoked by burning sheep dung. (Seriously.) The smoke aroma is really unusual, but actually quite nice.
I don't know which is the most distinct / unique beer, but did find this list of beer in Iceland.
The only thing I can add to the already given answers is for you to try out Ölvisholt's beer Jólabjór (or Lava if you find it).
Here in Sweden we get the annual Jólabjór at the state-operated monopoly Systembolaget. It's a discrete smoked beer imho.
I was on a quest to find some hoppy beers in Iceland and here is what I found: Hollie's Hobbies which has a huge selection of Mikeller beers.
I've had amazing beer from Iceland from a brewery called Einstök. Here is their website: The Einstök Brewery.
The Winter Ale and Pale Ale are one of the best that I've ever had and one of the few that got 5 stars from me on the Untappd App.