BuddyPress.org

I believe favourites are stored as activity meta information.

Therefore, you should be able to write an SQL query that does the job for you. Retrieving a list of activity IDs ordered by a COUNT on the number of times it’s been favourited. You’d then loop through the popular IDs retrieving the info you wanted (name, etc.) – I guess you could even pull that in the query.

I don’t know the field names / table names off the top of my head, but a scan of the DB should reveal it.

There may be an easier way via the API.