Crusty
Soon after you arrive in Iceland, a good example of the country's young lava formations can be seen on the way from the International Airport, to Reykjavik.

Iceland is sitting on top of the plate boundary between the N-American plate and the European plate and is, in fact, elevated oceanic crust, 2000metres above the surrounding seabed. This is because of so called "mantle plume" which pushes the crust upwards from below. Iceland is therefore a giant hotspot, much like Hawaii, Galapagos and Yellowstone National Park in the U.S.

The combined effects of the plate boundary and mantle plume are the source of all seismic, volcanological and geothermal activity in Iceland.

For comparison, the old lava flows in Iceland are very similar to ones that can be found in the islands off the western coast of Scotland, as well as parts of North-East Ireland.

Ye olde Thingvellir
Very close to Reykjavik you will find Thingvellir, where the Althing (parliament - the worlds first, by the way) used to reside.

Thingvellir are largely covered with lava, younger than 10 thousand years, just like the ness that you drive on coming from the International Keflavik airport.

A clear evidence of the aforementioned crustal movements in the country can be seen at Thingvellir. There the "Almannagjá", or Public's Gorge, shows very clearly how the ground has moved apart.
On your way there from Reykjavik, you drive from the so-called American plate, into a valley, which separates that plate from the Eurasian plate. This valley is where the Lake Thingvallavatn is to be found, and as the continents drift apart, the lake grows bigger and gradually drowns the valley.

Another result of the plate drift is earthquakes that occur quite frequently along the plate boundary.

Most recently, Thingvellir is pegged to join Stonehenge, the Great Wall of China, Taj Mahal and more in UNESCO's list of World Heritage areas. It was, amongst other places, nominated to join the aforementioned list and although a decision is not to be made until 2004, it seems quite likely to be succesful.

The main positive thing about this is that it would recognise Thingvellir as one of the worlds greatest historical places.

Lake Mývatn
In the North-East of Iceland (next to Reynihlíð, about 1-1 ½ hour's drive from Akureyri), not far from the Krafla volcano and the Námafjall and Hverfjall geothermal areas, you will find a Nature Reserve known as Mývatn. The Lake itself, as well as the surrounding area, is very popular with tourists and ducks alike (being one of the world's biggest duck sanctuaries) and is also the location of an ecological research institute (http://www.hi.is/HI/Stofn/Myvatn/engframe.htm). Another inhabitant of Mývatn, and a very important one, are the midges. These small flies are all around the area in vast numbers, so suitable equipment such as nets should be brought along (actually, the Icelandic word for a midge is "mý" -pronounced "me"- or "mýfluga", so you can see that they have even made it into the name of the place).

The geological interest in Mývatn comes mainly from its volcanic landscape, (this includes pseudo craters, lava fields and geothermal areas) as well as lying on the western edge of the volcanic zone coming from the South-West of Iceland. Near the Mývatn area you will also find Ásbyrgi which is thought to have formed in gigantic glacial floods known as "jökulhlaup". Others think Ásbyrgi was formed by the hoof of Sleipnir, the horse of the Norse God Odinn, when riding across Iceland.

The area has been shaped by the great seismic activity that surrounds it and you will find some exquisite scenery in and around Mývatn. If you are coming to Iceland to witness some geological beauty, Mývatn should definitely be high up on your list.

Huge amounts of algae also grow in the Lake. One of these are "Kúluskítur", an important algae which is the rarest form of the "Cladophora aegagropila" and presents itself as small (ranging from a few mm to 10-15cm) round balls of algae sitting on the bottom of the Lake. Apart from Mývatn and some very small quantities in an Estonian lake, this form of the algae is only known to grow in Japan's Lake Akan (on Hokkaido island) where it is very famous and even celebrated in a 3-day annual festival.
The algae were previously found in some other Icelandic Lakes, but have now all but vanished from most of them.

For an Icelandic website on the "Kúluskítur", containing pictures of the plant, have a look at http://www.hi.is/~marianne/ (an English version is apparently in the making, but not quite ready yet).

For some general pictures from Mývatn, try http://www.eas.ualberta.ca/elj/icepics/myvat.htm for accommodation information, see accommodation.html here.

Island life
Another very interesting place is Vestmannaeyjar; there you will find the main island Heimaey, which erupted in 1973, the effects of which can be seen very clearly with some houses still half covered by lava and the ground being very hot.
(So hot in fact, that it is used to bake bread amongst other things...)

Not far from Heimaey is Surtsey. Surtsey is a brand new island that finished forming in 1967 after 4 years of volcanic activity on the seabed.

Some amazing pictures exist from that activity, but unfortunately this was slightly before my time and I therefore do not have any.
However, thanks to the amazing kindness of the heirs of Dr. Þorleifur Einarsson we have 2 pictures here, which are from his book "Myndun og Mótun Lands" (cv link). and the third one (of Thingvellir) is also his.
Some more pictures can be seen at http://www.vulkaner.no/v/volcan/surtsey_e.html

The island is a Nature Reserve and used for scientific research and is invaluable in monitoring what happens to an island from its birth.

Many smaller islands have made an attempt at existence by forming in the ocean like that, but none have been able to withstand the forces of nature in their constant battle (i.e. wind and water). In fact 2 islands that formed at the same time as Surtsey and reached a height of 70m and size of around 0.5sq.km went underwater only a few weeks after they formed and are now around 40m below sea level.
Hopefully Surtsey will do better due to its size and possibly some preservation methods of man.

No Geologist (or anyone with an interest in geology) should miss the unique opportunity of visiting Iceland, and in particular Vestmannaeyjar (the Westman Islands).

For some more information on Surtsey, try the following text from a PBS show with Alan Alda

Hot and shaky toes
Previously mentioned seismic activity keeps the country's inhabitants on their toes but fortunately not much damage usually occurs, not least due to the way the buildings are built and where they are built (i.e. not too close to active areas).

The strongest earthquakes occur along the boundary in Southern Iceland every 100 years or so and they have often caused severe devastation. The last ones in these series happened in the year 2000, but they were not very strong and relatively few houses were damaged.
Also, any earthquake and volcanic activity is heavily monitored nowadays and warnings can be provided ahead of time, an even better reason to always check with the relevant parties before making any trips to possibly hazardous areas in Iceland.
Even more research is now starting into the Icelandic seismic activity, this time with an International group of scientists, led by the Icelandic participants and sponsored by the EU.

Also, at the time of writing, there has recently been some seismic activity around the glaciers/volcanoes Myrdalsjokull and Vatnajokull so you never know, there just might be a new eruption on its' way.

The seismic activity is usually linked to volcanic activity or geothermal activity in one way or the other. As an example, the geyser Geysir in Haukadalur had stopped erupting unassisted, until the earthquakes of 2000 breathed life into it and it now erupts somewhat randomly every 20 minutes or so, although the eruptions are perhaps not as big as they used to be.
(No worries though, as Strokkur - slightly smaller and sits next to Geysir - keeps on erupting every few minutes!)

There is also an incredible number of hot springs and other geothermal activity, all around the country. Whether it be mud pools, hot springs, steam vents or geysers.
These are all covered better in the "Hot Springs" category.

Fire and ice
As for the volcanoes, there are 27 active central volcanoes in Iceland, including Krafla (last eruption 1984), Hekla (last eruption 2000), Grimsvotn (last eruption 1998) and Eldfell (last eruption 1973).
Grimsvotn is one of the volcanoes that are covered by the glacier Vatnajokull, which covers many volcanoes.

These are discussed a bit more in "Volcanoes" and "Glaciers" respectively.

Lignite
Lignite, known in Iceland as "Surtarbrandur", is a form of brown coal, which is slightly more matured than peat and retains the ancient wooden texture of its predecessor. It can be found in the West and North-West of Iceland (mainly around the West Fjords) and was previously used for fuel. As an example, in World War I and II it was mined in a place called Botn in Sudureyri in the West Fjords' Sugandafjordur. Rich mines were to be found in other places around the West Fjord area, however, and mining was very busy for quite some time, but has not taken place for a few decades now. Apart from the aforementioned Suðureyri, the main mining places included Brjánslækur, Bolungarvík and Húsavíkurkleif.

And finally…
Lastly, like a bathtub without a plug, one of the lakes around Reykjavik, Kleifarvatn, is draining. It is believed that the abovementioned earthquakes in 2000 may have opened a rift, or a fissure on the bottom of the lake that drained the lake by more than 2 inches a week, revealing "…sulphur-rimmed thermal springs that spit boiling water and mud." Thankfully, the flow has slowed down dramatically since reaching its peak around the time the following article was written, but the facts presented still remain true.

Read the full report on National Geographic's website

Sources:
Myndun og Mótun Lands, an Icelandic book on Geology by Dr. Þorleifur Einarsson, published 1991 by Mal og Menning (see his text in English by the name of "Geology of Iceland"),

http://www.pangaeasci.com/_iceland.htm (a tour of Iceland geology)
http://www.myvatn.is/eng/main/ and http://www.reynihlid.is (about Mývatn)
http://www.hi.is/~marianne/ (about "kúluskítur")
http://www.sudureyri.is (Icelandic information on the town of Suðureyri)
and this Icelandic information on lignite, fossisls and more,

as well as my own knowledge and that of contributors (major contributor: Bergur Sigfusson).

For more general geological information on Iceland, have a look at
http://www.norvol.hi.is/
(the Nordic Volcanological Institute)
http://1.1911encyclopedia.org/I/IC/ICELAND.htm
(encyclopaedic entry on Iceland, including geological information)
http://www.ni.is/
(the Icelandic Institute of Natural History)
http://www.os.is/english/
(the National Energy Authority)
http://www.jfi.is/
(the Geosciences Society of Iceland)
and
http://www.geokem.com/volcanic-atlantic.html
as I looked at most of these during my work, I may subconsciously have picked up some details from them as well, without realising it. The abovementioned sites are therefore part of my sources as well.

If you are even more interested in the geology of Iceland, an amazingly good web page on the Icelandic naming of geosciences terms, as well as an actual Icelandic-English glossary can be found at http://pubs.usgs.gov/of/of95-807/geoicelandic.html

Lastly, some amazing satellite photographs of Iceland can be found at the NASA website here, including ones displaying dust storms and receding glaciers in Iceland.