Yes, there are two parts you'll need to build.
Part 1: A way to track which sites a person visits. This may be a httpmodule, or some JS/ajax in your masterpage, or a control in your masterpage or a webpart that is on the landing page of every site, etc. Something that will record in a database somewhere the userid, site title, site url, and datetime of the visit.
Part 2: Write your webpart to query the database and display the results. You can query the DB to only display the TOP 10 distinct urls and order by the last visited date descending.