Are you talking about the Ottoman Caliphate, or the idea of the Caliphate?

Succession of title:

• The Umayyad Caliphate proper was succeeded by the Abassids.
• The Umayyad Calphiate at Cordoba fractured - no claim made by locals or descendants.
• Abassids were succeeded by Fatmids everywhere but in Egypt.
• The Egyptian Abassids and Fatmids were succeeded by the Ottoman Caliphate.
• The Ottoman Caliphate was legally ended by Ataturk.

So, foremost, no one can claim the title this way. The Caliphate ended and no nation was even structured in such a way as to reclaim the title in 1924. At this point, the Middle East was still much more colonial than not. The title actually descended from Mohammad is dead and buried, as far as titles go.

So then that begs the question why no one like, say, Iran or Afghanistan, has claimed it since then. I have a hunch, which I think will be sufficiently uncontroversial. Like ibnTarikh said, there is al-Qaeda and certain pan-Islamic movements which want the caliphate reestablished, but most of that is well inside the twenty-year rule. Those groups, however, have not claimed the caliphate. There are groups that have and are considered exceptionally fringe.

My hunch is that no nation could actually claim the caliphate without alienating everyone else. The Muslim community would be instantly polarized by such a thing, not just along Sunni-Shia lines, but also along more self-interested political lines, because acceptance of the title of caliph also accepts the supremacy of the caliph. They would also antagonize the West, which has always had its hands in Middle Eastern affairs, from the establishment of colonies to Iran-Contra. As far as I know, there's not even been a serious rumor of a nation claiming the caliphate - it would be a terrible move politically. A pan-Islamist movement would first need to succeed to create the political unity.

It has. In the lines and charters of terrorist groups and umbrella groups using fundamentalist Islam ideology.

http://en.wikipedia.org/wiki/Islamic_State_of_Iraq_and_the_Levant

Quite alot of other groups, including Al-Qaeda, have expressed this idea as well. It is quite interesting. Its tantamount to us Westerners of European descent urging for the restoration for the Roman Empire. So is it reclaimed, in a sense. But I don't think its ever going to be implemented.