Wow, I can't even imagine dogs being banned...anywhere. Though I figured it happened in places. Still, I'm so used to there being at least two houses with a dog on nearly every street in my city that my brain just can't wrap around the idea of an urban area without dogs O vO;;
Other things Iceland has banned at some point:
* TV (but only in July and on Thursdays, ban lifted in the 80's)
* Beer (but strong alcohol and wine were ok)(ban lifted in 1989)
* Spaniards (only in the Westfjords and not really banned, but up until this April it was technically speaking legal to kill a Spanish person on sight)(not really though, we just had this one old law that ok'd it).