I spent three days in Iceland on a stopover, just to do Reykjavik, though I'd recommend double that amount if you're going outside of the city.

What I did in the city:

• Blue Lagoon - Obviously a must do!
  
• Reykjavík 871±2 (The Settlement Exhibition) (aka The Settlement Exhibition, Old West Side, Reykjavik, Iceland) - A fascinating museum that will teach you about the earliest history of Iceland.
  
• A whale watching tour from a company like Elding Whale Watching (Ægisgarður 7) to see the Minke Whales in Faxaflói Bay.
  
• There are tons of walking tours, most of which are free, and my favorite was the one which went to Hólavallagarður.
  
• If you want to enjoy the local experience of geothermal bathing/swimming, check out a nearby city pool like Laugardalslaug (on Sundlaugarvegur).
  

Sorry, this doesn't make a very helpful map, does it?
 Have a great trip!

(Edit: the map is now much better!!)

I went to Iceland for 8 days, and wish I had two weeks!

We spent 4 days around Reykjavik which was plenty to really explore the city. You could always find more things to do with more time, but by most standards, the city really is quite small.

We also took a group bus trip out to see the Northern Lights and it was worth the time, although depending on the weather and the time of year you might have a different experience.

There are also many tour groups that will take you through the "Golden Circle" area (Þingvellir, Gullfoss Waterfall, Geysir) all within one day.

For us, sitting on a bus with a bunch of people and not being able to go at our own pace wasn't quite what we wanted. We booked a self-guided tour with Nordic Visitor and can't say enough good things about them! They provide you with a car, gps, mobile phone, and will reserve bed and breakfast type places along the way. You are free to chose which places you want to go and how long you stay there. In addition to the above, we also explored the southern coast including the small town of Vík with its amazing black sand beaches and basalt pillars and other formations. There's numerous waterfalls in the area (Seljalandsfossand Skógafoss are some of the better ones) as well as some very unique viewpoints around Dyrhólaeyjarviti. We came back along the Southern Coast with a stop at the very popular Blue Lagoon (which isn't in Reykjavik but is near the airport. Many people spend their last hours in Iceland there before heading to the airport to depart).

For the most part, the only driving around Iceland is on a perimeter road that mostly follows the coast. If we went any further east, we would not have enough time to complete the circle (7 days rushed, 10-14 days if you really want to explore) and would have to loop back the way we came. I would love to go back and explore the northeastern part of Iceland for places unlike any other on Earth (Dimmuborgirand Dettifoss just to name two).

Of course, there's much to see in the north western parts as well... I think if you do any research and spend anytime exploring, you will always wish you had more time!

If you fly Iceland Air from the US to one of their destinations in Europe, you can take advantage of a free stopover up to 7 days. http://www.icelandair.us/flights/stopover/

I did it and stayed 6 days which was a good amount of time, but surely not enough to see all the great sights and attractions of Iceland. It's one of my favorite countries I've visited in my life, and I've been to many! You won't regret it.

I took a 5 day trip with friends in March- Here are my Top 5, in no particular order:

1).  Glacier hike- tons of different tour operators. We booked through Extreme Iceland and they sub-contracted to someone else but our guide was fantastic.We went at Sólheimajökull

2). Þingvellir National Park- was gorgeous in the snow, I bet its even better in the spring/summer/fall

3). Kolaportið Flea Market - Reykjavik. Nothing fancy or high end, but a good "local" experience.  I got a great deal on a wool sweater here.

4). Blue Lagoon- All tourists, and by no means a natural wonder as its a man-made lagoon but it is by far the most relaxing day I've ever had traveling. 

5). Gullfoss Waterfall-  huge waterfall along the "Golden Circle"  

And one more - Jökulsárlón-  Glacial lagoon.  I didnt actually make it here b/c of our short trip, but have heard repeatedly that it is a highlight

If you are going to spend your time traveling the entire country, you can spend 8-10 days trekking through glaciers, waterfalls, and volancoes. I mostly stayed in the capital Reykjavik.  Most do's can include going on an Icelandic horse tour, lots of tours surrounding the waterfalls, Blue Lagoon is a must see. The capital city is super small so take advantage of all the off road excursions to explore a lot of nature trails and waterfalls.