Not exactly what you are looking for, but there's a great plugin for google analytics. It will tell you how long visitors spend on your site, where they are located, how they found you site, how often they come back, number of page views, and much more. It just doesn't associate these stats with a username.
Making the plugin you need would probably require some data model changes and I haven't seen many plugins that do that. You would need a new field in the user table just to keep a running tally of how much time they have spent logged in, or a entire new table to record all of the times each user has logged in and the length of each session. Then change login.php accordingly.
I wasn't able to find anything like that, but maybe someone else can be of more help.