Suppose I send you a link to a page I own. I start this thing on said page and track what you do with the rest of the session on the off-chance that you do something sensitive with it. It's like a single-tab key/screenlogger. Combine this with traditional phishing methods (which already work) and you might get valuable data. It's going to be at least as effective as current phishing methods, with the added advantage of not asking for personal data on the landing page as well (so users don't get scared off).

A similar attack would be to override the back button. You know those sites where the back button takes you to a redirect that takes you to the same page? Take one of those, but on the redirect page save the referring URL. Then when the user hits back, have the redirect page start the session sharing and redirect to the referrer. Sounds plenty dangerous to me.