Hopefully by "off-road" you meant "off tarmac onto rough roads".

Yes, that is what I meant. I apologize for the confusion. I would not want to harm the environment in anyway while there.

I am also intereseted in a car rental, but could no decide so far...maybe i'll try the cheap jeep rental...
@dassi1 are they really good, are they trusty?
BTW: What is better...to bring EURO or the native money with me? Can you help me with this question?
Thanks

Withdraw ISK on you debit/credit card for those very, very rare occations where you need cash (Iceland is the very strong "plactic"-country)
If youi really by some special reason want to travel around with cash: You are from Switzerland?? Bring Swiss Francs - never exchange twice - and never try to buy ISK outside Iceland - they tend to take you for another 10-20% outside Iceland if you can get the currency at all - remember how "small" the currencey is (3-400,000 inhabitants).

I have so far not heard anything rely bad about them but I will ask people that rent trugh me to tell me how it went. I had a car from them today and it worked out fine :)
Bragi
If you plan to stay on the ring road, there is no need for 4x4. Just a good car with at least 2 liter engine (stay away from the smalles cars). If you plan to leave the ring road and aventure in to the gravel roads of Iceland, 4x4 would be better option.
If you plan for 4x4, the one I really like is Nice cars (http://www.nicecars.is), but if you just want to rent cheap car you can pick cheaper rentals such as http:///www.sadcars.is. Be aware that they quote the price with out any insurance, so you need to calculate the full price to compare.
