Ideas to build a SharePoint Most Popular Documents webpart
1. IIS Log
a. we use a logparser to push iis logs to db monthly for reporting. tweak the code to push only document read info to a db table daily.
b. build a webpart to read the sql table.
2. Audit logs (bad idea)
a. turn on site collection audit logs to track document view.
b. use audit log object model to read the info you need.
3. Site collection usage reports -> i dont know if the reports store the document information. I dont think it does, maybe worth a check.
4. Complicated approach, but could be extended,
b. Use the list view webpart / custom webpart to display the list view.