Is the number of private pilots increasing or decreasing?
The statistics for the number of pilots in the US is fairly easy to come by, The Aircraft Owners and Pilots Association published a report on the number of FAA certified pilots. This shows a general static trend over the 10-or-so years preceding the report in 2011

Year    | Total Pilots
======================
2011    |   618,660
2010    |   627,588
2009    |   594,285
2008    |   613,746
2007    |   590,349
2006    |   597,109
2005    |   609,737
2004    |   618,930
2003    |   625,011
2002    |   631,762
2001    |   612,274


The graph shows the total number of pilots since 1929.



For Europe, this statistic is a little harder to come by. In general, Aviation in Europe is controlled by the European Aviation Safety Association to which pretty much all European countries are members, with a few having a working arrangement to sync up their procedures/licensing. The EU, and its associated agencies are typically bureaucracies at their best (worst!) and so there is unlikely to be a single register of the number of pilots. 

For example, some elements of aviation (although NOT Licensing) is still managed by the UK Civil Aviation Authority. With all the various european and intra country agencies involved in European Aviation it will be tougher to get figures for the number of pilots.

Internationally your problem is moreso. With tens of different agencies involved in the Flight Crew Licensing, you may find it harder still to get some accurate figures.