Where can I find statistics on the percentage of the population that were serfs, ideally broken down by country/region and by year? Even very rough estimates would be helpful, but unfortunately I've found even these to be hard to find.
Simply put, there is a distinct absence of any official counting being done, by anyone, until long after your period of interest - with the notable exception of the Domesday Book commissioned by William I (The Conqueror) in 1086.
From my comment just now on the accepted answer to Are there equivalents of the Domesday Book for other (French or German) duchies?
Germany (or various principalities of the HRE if you prefer) seems to have had Europe's first "national" census': Nuremberg in 1471; Brandenburg-Prussia starting in 1683 counted its rural population with the first state-wide census between 1719 and 1725. Also, this might be a useful second link for the Domesday Book.
The accepted answer to Did every medieval village in Europe have a manor, castle, or other type of lord's residence? also bears on the current question.