This question was posed to me earlier today and it got me thinking. I don't think that most people I know would argue against the notion that evolution has infact happened. Assuming that evolution is true, I think the more obvious questions with regards to evolution should be: are we still evolving, and if so, how much?
From a purely biological perspective with regards to physical characteristics, I would argue that the answer would be "not really", and I'll explain that in a minute.
The sociocultural aspect of our collective societies is evolving; of that there seems to be little doubt. Humans have always evolved culturally. (A fascinating read on the overall topic of human civilizations and evolutionary behaviors is Guns, Germs and Steel by Prof. Jared Diamond). In our modern digital world it seems as though our current cultural evolutionary process is leading us to world that is more close-knit and united.
One of the interesting side-effects of becoming more multicultural as a species is that it invariably leads to interracial breeding on a scale not seen before. There have been several studies on the impacts of this. A quick survey of the census records in the US also show this to the be the case as more and more immigrants from other countries move here. Cultural behavior, and certainly multicultural behavior certainly shapes our genetic makeup as we trade and mix DNA with an ever-growing host of potential mates that was not readily available 100 years ago. The October 2011 issues of Psychology Today discusses this very issue citing a 2003 study conducted by Joan Chiao of Northwestern University. The study linked DNA to behavior in ways that were not so expected; such as China's idolization of Communism and the Western culture's adoration of independence. These behaviors are now understood to be driven by genetics. By that logic, changing our genetic makeup will certainly change our behavior. As other's pointed out, I'm not convinced that this would make us any less pliable or adaptable as a species.
Certainly having a genetic admixture will result in noticable physiological changes; skin tone, hair color and type, height, etc. But, from a biological standpoint the question that I find myself asking is: so what? Okay, so my descendants will one day have a skin tone that is more coppery than my fair Irish skin. Does that afford them any special advantages? No. Does having a different height or a different hair type help ensure their survival? Not really. In today's technological world medicine and medications have gone a long way in stamping out things which would have eradicated "weaker specimens" even just a hundred years ago. From that standpoint the introduction of "weak" genes into the genepool persists whence it would have been stamped out before.
From a fundamental standpoint the purpose of evolution is to provide those specimens with the strongest genes the best chance to reproduce and spread healthy offspring. From what I've seen none of the physiological changes that are occurring in our current admixtures of genes seem to be doing this. Sure, they change our physical appearances, but that's about it. This example dealing with shark Genetics (http://www.nbcnews.com/technology/futureoftech/australias-hybrid-shark-reveals-evolution-action-904726) reveals a more arguable demonstration of evolution in action; the sharks are adapting to endure different temperature climates than what they were otherwise used to. What primary advantages does the admixture of modern human genetics provide us? We have houses to shelter us from the elements, we have medicine to cure our illnesses. Even within the human species the sexual dimorphism of Homo Sapiens is already far less pronounced than in other species in our genus. The rest of our traits are spread across a wide array of polymorphic attributes.
From a Taxonomy viewpoint the consideration of the human species in general is rather fascinating. For every other species on the planet we break down their taxonomical classifications into distinct sub-groups based on geography and physical characteristics. For example; the Willow Warbler is divided into three distinct sub-species that are genetically identical and the only differences between them is the location of their habitat and the coloring of their plumage. Their skeletal structures are identical. Humans, Homo Sapiens Sapiens in particular, have a wide range of skin colors, hair colors, natural habitats, slightly genetic makeups that, although compatible, are slightly different. And yet, we are all lumped into the exact same genus and sub-species despite obvious polymorphic differences. Surely this muddles the question of evolution and genetic admixture. If you were to break human beings into separate sub-species based on their genetic haplogroups, then because the specific traits that are being analyzed are so narrow, it would certainly argue a stronger case for continuing evolution.
As you might have guessed I can relate to both sides of the debate that humans are and are not evolving. I personally don't have a strong opinion about it one way or the other. However, I do feel compelled to point out that in my own studies of evolution over a long period of time the driving factor in pushing major physiological changes within a species seems to be either radical climate change or natural disaster on an epic scale (like a giant meteor). Fossil records of human settlements show that our physiology has remained largely unchanged for the last 200,000 years. If this is true, then how much evolutionary process is truly going on now within the span of a few centuries?