Recently I switched my personal email hosting over to Google's Gmail and I am so happy I did. It's fast, really easy to use, has excellent spam protection and is free (of course).
Some people are wary of Gmail because of the "sponsored links" that appear to the right of an email when you read it. They think that Google is mining your email to determine what ads to show you based on an analysis of the content of your emails. That's not the case!
What Gmail does is look at the content of the specific email you're looking at in realtime and show relevant ads based on that analysis. It's a subtle but very important distinction.
It's no different than the way sponsored links work when you perform a Google search. Google isn't storing or analyzing long-term information about the contents of your emails and never will. They only show you ads when you open an email to read it. Their ad servers decide what sponsored links should be displayed at that moment, then when you close the email, that's that.
I can understand the reason for concern and honestly I think Google could do a better job of explaining how Gmail ads work.