Really interesting and well researched piece published on Moz (written by Philip Petrescu) about how many clicks each position in the search results page receives, combined with some analysis tools to help you predict demand.
The graph below is a summary of the data for desktops. On average, 71.33% of searches result in a page one organic click. Page two and three get only 5.59% of the clicks. On the first page alone, the first 5 results account for 67.60% of all the clicks and the results from 6 to 10 account for only 3.73%.
Interesting, not only is the click-through rate (CTR) slightly lower on the first page, but the CTR for mobile searches actually rises on the 2nd and 3rd page.
Particularly relevant for our kinds of clients, the difference between "brand-related" and "generic" searches is dramatically increased. For branded searches the first result is almost always associated with the brand's website, which makes it the obvious choice for most users and very hard to miss.
There are a lot more statistics and charts provided (plus a whole debate) and you can read the whole piece here.