Your priority will be to keep warm and you'll almost certainly invest in a famous woolen jumper... before being tempted by the jewellery and the country's culinary specialities.
At the risk of disappointing you, in Iceland it's cold. One of the big classic souvenirs to take home is therefore a handmade Icelandic woolen jumper. As it's so thick it protects against the extreme temperatures and is often decorated with varied geometric patterns. You can also take home several products from the famous Icelandic spas. They are 100% natural and exceptionally effective.
Naturally you'll be enjoying salmon all throughout your trip to Iceland. Don't hesitate to take some home to make the trip last even longer. You can also buy smoked lamb and herrings to brighten up your winter evenings. Finally, in terms of drinks, potato liquor and Icelandic vodka are two musts, so get some for yourself for when you return! Personally, I also chose to buy one of their cheese graters. Warning: I'm not just talking about any cheese grater here, but a grater which any self-respecting Icelandic person should own. This wonderful utensil allows you to get extremely thin slices of hard cheese: believe me, your classic cheese on toast will be transformed!
If you've enjoyed the Friday night concerts in the Reykjavik bistros (a must visit city during your trip), take a CD of Icelandic music home with you. Whether it's traditional music or pop rock, the inhabitants of Bjork's native country excel. In terms of presents, you'll have the pick of the crop between key rings, Icelandic mugs, and original t-shirts which are sometimes very funny. Icelandic people also create amazing hand-made jewellery which often have patterns inspired by the Viking history. Finally you can also find jewellery made from volcanic rock.