Yes, but not significant in the sense I am using it here.
Natural selection is changes in the frequency of genes not planned by wise and well-intentioned humans.
Significant natural selection is when this leads to a shift in the fundamental values of the human race.
In that case, I would say that the answer is clearly "yes," in the sense that significant natural selection is taking place at a rapid clip in the present day. For example, the percentage of people in the world with blue eyes has surely dropped significantly over the last 100 years.
I was browsing my RSS feed, as one does, and came across a New York Times article, "A Village With the Numbers, Not the Image, of the Poorest Place", about the Satmar Hasidic Jews of Kiryas Joel (NY).
Their interest lies in their extraordinarily high birthrate & population growth, and their poverty - which are connected. From the article:
From Wikipedia:
Robin Hanson has argued that uploaded/emulated minds will establish a new Malthusian/Darwinian equilibrium in "IF UPLOADS COME FIRST: The crack of a future dawn" - an equilibrium in comparison to which our own economy will look like a delusive dreamtime of impossibly unfit and libertine behavior. The demographic transition will not last forever. But despite our own distaste for countless lives living at near-subsistence rather than our own extreme per-capita wealth (see the Repugnant Conclusion), those many lives will be happy ones (even amidst disaster).
So. Are the inhabitants of Kiryas Joel unhappy?