Google has two similar projects that show search trends over time: Google Trends for comparing keywords and Google Insights, which explores sub-searches within a trend. It can be difficult to determine the difference between them, but in comparing the keywords, we can tell you which one developers most want to have an API: Google Trends.
Strangely, Google Trends was unable to provide the above graph due to insufficient data. However, Google Insights happily displays the current interest of each search term. Consistently, developers have been more likely to search for Google Trends API than Google Insights API. Unfortunately, neither exist.
What developers want, they find a way to get. There's a python library to extract the Google Trends data. Those after a Google Insights API aren't so lucky. The best I can find is a forum thread with scientists begging for data. One even offered Google $1,000 per year.
Of course, it's dangerous to hang your hat on something unsupported. For those willing to walk out on a limb, we list 19 unofficial APIs. And the search giant is no stranger to the idea, since it maintains an unofficial, secret weather API.