Iceland sits atop a divergent ocean- ocean boundary. But there are not many islands which are formed along a divergent boundary. Why is it so? Why do not mid ocean ridges often rise above the sea surface to form islands? Why are islands more common along convergent plate boundaries where they often form archipelagos?
The reason islands don't form along divergent plate boundaries is that these boundaries are at the bottom of the sea, and usually quite deep. Although mid ocean ridges are volcanic, the magma doesn't get a chance to pile up and reach the surface because the plates are not static. They are slowly spreading apart, and the magma is needed to form fresh oceanic crust between them. The logical place for sea floor spreading is at the bottom of the sea. I only know of one other place where this happens on land, and that is in the Afar region of Ethiopia.
Islands are common on convergent plate boundaries because volcanism is common on convergent plate boundaries. This is where oceanic crust is subducted. Volcanoes and other phenomena connected with subduction tend to form islands. The Pacific 'ring of fire' is an example of this.
Iceland isn't only situated on a divergent boundary (which in itself can rise up to shallow depths because of higher static and dynamic lift btw.) but also on a (postulated) pretty deep rooted mantle plume that may produce enough magma to rise to subaerial heights.
Edit: The magma that erupts at an ocean ridge is "welded" to the sides ("sheeted dykes"). According to the actual understanding, it is the pull of the subducting plate(*) at a convergent boundary that drives ocean spreading, thus "stretching" things rather than causing them to pile up. The rates at which magma is produced at a ridge is too low to fully compensate for that.
Islands, if not forming an arc and situated intra-plate, frequently have a plume under them or are fed from fingers of a plume from the side. In the case of Iceland it is (probably) the plume (in co-operation with "viscous fingering") that produces enough material for a subaerial edifice.
(*) ... before somebody objects: not necessarly the plate connected to that ridge, but another one elsewhere, and the earth as a whole can't shrink or grow and also isn't exactly hollow ;-)