Where People Look & Click: In-Page Analytics in Google
The "In-Page Analytics" option under "Content" will show you which links on any given page are getting the most clicks.
Note that Google can tell how many visitors go from one page to another, but not which of two or more links to the same location is getting more clicks; duplicate links will all show the same number.
The Unitarian Universalist Association uses another tool, called Crazy Egg, to more accurately track clicks by location within a specific page.
Heat maps show that clicks on UUA.org follow the standard that holds across the web: while content in the right sidebar gets some notice, the attention it receives pales in comparison to that given to the classic "F-shape" browsing pattern: Heat Map of a UUA.org Page (PDF).
Another good tip to remember is that web readers tend to avoid looking at callout areas that look like ads; instead they focus on the body of a page.