[T]he (preliminary) 1000 Genomes paper came out last fall. . . almost all the variants that have reached fixation in different groups are (or will soon be) known. . . . there are . . . many more differences in fixed variants (72) between E. Asians (CHB+JPT) and Yorubans (YRI) than between any other pair of groups: only 2 between E. Asians and Europeans (CEU) and 4 between CEU and YRI. This means that there are a bunch of variants that are fixed differently in YRI and CHB+JPT but both versions remain in CEU.
I suggest a cause for this in a comment to the post:
There is a thin but measureable level of admixture between Africa and Europe, probably from the Neolithic, possibly as late as the Roman Empire, the Moorish presence in Spain, and the Ottoman presence in the Balkans. There was probably European introgression into East Asia in the early Bronze Age in Northeast Asia and later via the Silk Road. There are a handful of East Asians buried in Rome from classical times and would have been admixture via circumpolar societies (e.g. Uralic), the Turks, the Mongols and the Silk Road. There was no comparable admixture between Africa and East Asia.
Of course, there are all sorts of genes that have reached fixation (i.e. everyone has the same single variant of the gene), all modern humans, and there are a fair number of genes that have not reached fixation (i.e. there are multiple variants floating around out there in every population).
Selective effects can lead to fixation, but so can founder effects and a certain amount of random chance in small populations. Rate of population change is also important. Expanding populations tend not to lose variants of a gene. Contracting populations do tend to lose low frequency gene variants. Human population history shows strong signs of serial founder effects with fairly low effective population sizes at various points along the way.
It is also worth noting that 1000 genomes still miss quite a few rare variants, which incidentally, have surprisingly little overlap between major continental populations (suggesting low levels of post-divergence admixture).