Most flights to and from Iceland are operated by Icelandair, especially during the winter. In the summertime there are various charter flights operated.
For the last 2-3 years, Samvinn-Travel's "Flugfrelsi" (= flight freedom) has offered cheap flights to destinations in Germany (Berlin, Munchen, Frankfurt), Denmark (Copenhagen), Spain (Palma, Alicante), Portugal (Faro), Italy (Rimini) and Greece (Rhodos). Last year, Air Atlanta Icelandic handled most of those flights (all except those to Germany), but due to fewer passengers this year, Icelandair among others make those flights now. Flights to Germany have been operated by Aerolloyd.
Go Air (www.go-fly.com) operates daily flight between Iceland and London during the summer.
There are some more. To see for yourself, check out http://www2.mbl.is/frettir-ifx/frettir/flug
. There you can see a realtime schedule of flights (displays flight traffic in the next 24 hours or so). The page is in Icelandic (All you need to now is that "Brottfarir" = Departures, and "Komur" = Arrivals. The rest should be easily understood).
Reykjavik Aviation Photography - Just bring the aircraft to us and we'll photograph them! :-)