I know there are a few people who read this blog with serious intentions to move here, and since I have had emails about this a bunch of times, this is the summary of what I know about renting in Reykjavík after working on this for several months. First of all, I should explain that unlike in Boston, the cost of owning a place is equal or less to the cost of renting, so anyone who possibly can own, does. As an immigrant still on a temporary visa, I can not yet, so I'm stuck with what is often the dregs of the housing market.
If you're looking for your own place (as opposed to renting a room in a shared place), they generally fall into two categories. First, there's the perennially for-rent places, usually owned by an Icelander abroad, or as some kind of second property for income. I saw one of these that was in a fantastic location, but was tiny, on the ground floor (people walking by directly outside your window feels not-so-safe, even in small-town Iceland), and contained dingy carpeting that looked like leftovers from a seventies-era warehouse (burnt orange! More awakening than coffee). There was also no way to to do laundry, which in Boston was not an issue with all the laundromats usually available in neighborhoods. Here, everyone's got laundry in the house or in the building, so laundromats pretty much do not exist. When I asked about it, the owner said, "well, the last guy just went to his mom's to do it". Not so easy when my mom's laundry room is a day's trip by plane from here. This place was also 75000isk/month, pretty expensive, even if you did get a back yard. I've since heard of another place almost exactly the same a few streets over.
The second category is the going-abroad-to-study category. These are nice places but only available for a limited duration of anywhere from six months to two years. They're also a person renting their home directly to you, so in many cases it comes down to a sort of popularity contest, or a who-knows-whom issue. Large management companies with a plethora of almost-identical apartments available (as my last place in Boston was) do not exist here.
There are exceptions to this, like the last place I lived, which was owned by a fisherman who was never in town but bought it since it was a great location and newly built. I know a few other people who have gotten lucky with this kind of thing- a family that moved to New Zealand thinking they would come back in a year or two and then just decided to not come back, leaving their house with all furnishings behind.
So, how to find these places? There are a few websites, like Morgunblaðið's classifieds, where the apartments for rent in Reykjavík are intermixed with summer rentals in Spain, houses in Húsavík, and flats in Akureyri. There is also leigulistinn, which you must pay 3500 krónur a month to have access to, and the places go fast there. After being in Craigslist-land the thought of having to pay so much makes me cringe, but they do have the most comprehensive listings there. A few other sites have tried to get into the business but remain kind of paltry on the rentable places, unless you want a two-floor penthouse or a basement in Árbær (=really far from downtown). Then, the better way (and where I found mine) is internal distribution lists and friends-of-friends. Since most of the places for rent are owned by individuals, they want to know they're having someone trustworthy in their home while they're away, so personal recommendations count for a lot.
And finally, what do you get with an apartment here? In addition to the living space, you'll get laundry room space in the basement if it's not in the apartment already. This is a fairly common arrangement, particularly in buildings from the fifties or earlier. Each resident has a designated hookup for their own washing machine in a shared space in the basement. In the larger buildings, there might even a separate drying room near the steam pipes. Dryers are not so common here as in the US in these places. You'll also often get a storage cupboard or room somewhere, the much desired geymsla, for your boxes and suitcases. In cases where someone's going abroad for a few years, they might be using this entirely for themselves or you'll be sharing with them. Appliances are not a given (except the stove), which is part of why renting from the second category is often easier, since the people going abroad don't usually take their fridge along.
The prices are high here, but after being in Boston I definitely don't feel like I'm getting a bad deal. I'm paying less for a bigger place with more accessories, in about the same type of neighborhood. I could have chosen to live further out of town, where the prices are usually able to get a larger place, but the difference is not significant, and I personally prefer the old details and the immediate by-foot access to all manner of downtown experiences.
So there you have it. You now know everything I do.