Central Asian states will descend into poverty, having nothing else keeping them afloat. Some of the bigger ones, like Saudi, will probably be fine enough for a long time afterwards though, thanks to clever market manipulation they've got some cash in the bank.
Dubai is probably the most forward thinking, turning the entire country into a must-see tourist destination for post-oil cashflow.
South and Central America have been transitioning themselves to become service and tech economies, so good on them, deflating a bubble instead of popping it.
North America doesn't have much stake in it at all, and we'll probably be the first to fully move past oil anyway. Europe will be totally fine as well.
Africa won't notice a difference either, not to say that's a good thing.