It may surprise you to learn that public toilets are newsworthy in Iceland – the shortage of them hits the headlines every so often, and stories of tourists doing their business in public, in inappropriate places (eg car parks and cemeteries), are guaranteed to madden the locals. Many Icelanders view the increase in human waste being found in nature as being directly linked to campers and campervan travellers who shun campgrounds, and this has led to new laws prohibiting such camping.
Reykjavík and larger towns have public restrooms, but natural sights (including major Ring Road sights such as Jökulsárlón and Seljalandsfoss) often have too few facilities for the increasing number of visitors. Long queues can form at the small number of toilets available, especially when buses pull in. There are also long stretches of road without any facilities at all (eg the 100km stretch of Ring Road between Höfn and Djúpivogur).
Our advice: plan your trip well; stop at facilities wherever you see them (eg N1 gas stations); and be prepared to fork out a small fee (eg kr200) for the use of some facilities. Do not do your business in public because you'd rather not pay. If there's an emergency, find an appropriate place (do not dig up fragile land) and do not leave your toilet paper behind.
And keep your fingers (and legs) crossed that Icelandic authorities tackle this issue soon!