It depends on where you want to go. Small cars are restricted to the area directly around Reykjavik. You're able to drive out to Geysir and Thingvellir no problem, but you will not be able to drive to the remoter locations of Iceland. For that, you will need a 4x4. Things might have changed since I was there last, but I remember that detail very clearly. It was a cover on the steering wheel that told us that, along with advising us that "Sheeps do not obey road laws".

Also, if you intend to go into the central part of the country, you will be fjording rivers once the road stops. It's best to have a guide. Insurance doesn't cover pulling your 4x4 out of the river/water damage from that I remember reading.