If we do not rent a car, what is the least expensive mode of transportation from KEF Airport to downtown Reykjavik?

Your best bet would be one of the airport shuttles.

There are a few to choose from and they're all much of a muchness cost wise, however depending on where you're staying, some of the shuttles drop you off at the hotel front door rather than at some point equidistant from the hotels in the vicinity.

You should expect to pay around the equivalent of £10 for a one-way trip, but if memory serves you can buy return tickets which would work out cheaper in the long run.

Have fun!

And what a mind-boggling trip that journey from Keflavik Airport to Reykyavik was the first time I did it - all barren lava flows - nary a tree or much vegetation in site - looks like the moon - stark but awesome in its own way. With the cost of petrol in Iceland being sky high you'll save loads on taking the bus over renting a car.

catch the bus, get a clear idea where your hotel is and make sure you get off at the right stop. But watch the weather. I've walked through Reykyavik at 3 in the morning (broad daylight in the summer) but I'd hate to do it in snow.

The Grayline bus transfer at about $32.US p.p. roundtrip is priced lower than the Iceland air transfer. Are there local shuttles that would be cheaper? Can they be reserved ahead of time? Is there a certain local bus number that goes directly to downtown Reykjavik?