It has been suggested to me that human evolution has slowed or halted because natural selection no longer "weeds out the weak" before they get a chance to reproduce.
However, there are still places in the world where the unnatural selection of famine, disease and war kill off children and young adults in large numbers.
Have we observed it happening?
Have we seen it occurring in the last ~150, i.e. since the last time there were famines in e.g. Europe? No. 150 years are only six generations. You need to have sequenced a lot of genomes to see evolution, i.e. changes in allele frequencies, over as few as six generations - unless there has been a catastrophe that has wiped out specific parts of a population. Currently, work is still ongoing to sequence even 1000 genomes. Current data allows identifying selection over the last few thousand years, i.e. ~100 generations, for example in adaptation of people in the Andes and Tibet to life under low oxygen conditions (see this article from PNAS).
In short, we cannot observe evolution through natural selection (which Darwin termed "natural" to differentiate it from breeding) in humans over very short timescales at the moment. However, we can observe evolution, i.e. change in allele frequencies, due to "breeding" in humans, such as caused by sex-selective abortions, which is shifting the ratio between boys and girls in some countries.
However, there is theoretical and empirical evidence that evolution is most likely speeding up due to the growing human population.
EDIT
A recent paper in PNAS describes observable microevolution in humans between the late 18th century and mid-20th century. The authors use phenotypical analysis and statistics and conclude that the changes are not compatible with genetic drift.
It is often claimed that modern humans have stopped evolving because cultural and technological advancements have annihilated natural selection. In contrast, recent studies show that selection can be strong in contemporary populations. However, detecting a response to selection is particularly challenging; previous evidence from wild animals has been criticized for both applying anticonservative statistical tests and failing to consider random genetic drift. Here we study life-history variation in an insular preindustrial French-Canadian population and apply a recently proposed conservative approach to testing microevolutionary responses to selection. As reported for other such societies, natural selection favored an earlier age at first reproduction (AFR) among women. AFR was also highly heritable and genetically correlated to fitness, predicting a microevolutionary change to- ward earlier reproduction. In agreement with this prediction, AFR declined from about 26–22 y over a 140-y period. Crucially, we uncovered a substantial change in the breeding values for this trait, indicating that the change in AFR largely occurred at the genetic level. Moreover, the genetic trend was higher than expected under the effect of random genetic drift alone. Our results show that microevolution can be detectable over relatively few generations in humans and underscore the need for studies of human demography and reproductive ecology to consider the role of evolutionary processes.
Yes, we have seen it in resistance to diseases. Diseases spread readily in Eurasia, and over time resistance built up to them. When the colonization of the Americas started, these diseases arrived at the same time in a population that hadn't encountered them before and this had no resistance. We don't know how many died, but some estimates go as high as 95% of the indigenous population.
See also the relevant Wikipedia article.
