According to Huebner (2005) the per capita rate of innovation has been falling steadily since 1873 (it doesn't look quite like that from the chart below, which is just of patents, because patent laws changed a lot during the period). He constructs an index of innovation by looking at independently-created lists of events in the history of science and technology and from US patent records and compares them to the world population.
Woodley (2012), looking at the numbers for a different purpose, compared them with three alternative indices of development, and found that they correlated well with different numbers gathered for different purposes. For example, they correlate highly (with a coefficient of 0.865) with the numbers in Charles Murray's Human Accomplishment, which quantifies contributions to science and arts partly by how much space encyclopaedias devote to particular individuals.
It also correlates 0.853 with Gary (1993)'s separate index, which was computed from Isaac Asimov's Chronology of Science and Discovery. Finally, it correlates with another separate index, created in Woodley (2012), computed from raw numbers in Bryan Bunch & Alexander Hellemans (2004) The History of Science and Technology, and divided only by developed country population numbers in case there is something special about them in creating innovation.
The result seems quite robust, although I am hoping my friend Anton Howes (who has an excellent new blog on the industrial revolution, and is working on a PhD on innovation and the industrial revolution) will construct an even better index. Should we worry?
There are a few reasons for optimism. Firstly, the population is going up, so per capita declines in innovation are being counteracted by there being more people around to innovate. For example, even if Gary (1993) is right in thinking there has been a roughly five-fold decline in per capita innovation in the past 100 years—there has been almost a four-fold increase in population, balancing much of that out. Secondly, some of the innovations we are getting will allow us to raise our IQ—including genetic engineering and iterated embryo selection—and we know that IQ is one important factor in innovation. Thirdly and finally, there are many countries (such as China and India) who have so far been too poor to have many of their population engaged in innovative activities, but who will surely soon be.