I would like to see Ancestry devote a place on the user's homepage that would display a scrolling list of any events in his/her family tree(s) that happened on "today's" date. Additionally, if I had already utilized Ancestry's "calculate my relationship" tool, this would also indicate my relationship to the person in the event, and maybe show the primary photo for that person. For example:

May 3, 1929
Your great, great grandfather, John Smith was born in Somewhere, Indiana.