I just wanted to plug Orange Car Rental Iceland here because it doesn't look like they have a TripAdvisor presence yet. The experience I had with them is one of the highlights of my time in Iceland-- they picked me at the airport, made me coffee, taught me some Icelandic phrases to get around with and they even drove out from Keflavik to Reykjavik to pick up the car from me when I was finished with it. The car was brand new with studded tires, which definitely helped in the snow and ice I drove through. (Interestingly, the radio stations play a lot of American/English top 40, so when I was driving I felt like I was back in the States.)
All in all, the price was great, the car was great, and the guys at Orange treated me more like a friend who came to visit them than a tourist there to do business with. I can't recommend them enough!
Let me know if you have any questions about driving in Iceland too, it was a lot easier than I expected it to be after reading all the dire warnings about the road conditions in the winter, even when a big storm rolled in.