What effect does driving convictions have on a PPL?
In the US, driving while under the effects of alcohol and drugs may have a adverse effect on your medical certificate.  Additionally, I have heard (from an FAA inspector) second hand that in one instance, someone who had a driver's license revoked for a large number of speeding and reckless driving circumstances, eventually had a medical certificate revoked.

Arrests, and administrative actions require reporting to the FAA Aeromedical branch within 60 days and failure to do so can not only affect a medical certificate, but also pilot certificates, instructor certificates, A&amp;P certificates, controller certificates, etc.  The penalties for non-reporting are significant.

Addendum:  US pilots are required to make TWO reports relative to substance and alcohol issues.  Part 67 requires reporting notifications, arrest, etc. to the Aeromedical Branch. Part 61 requires a notifying Security at FAA upon conviction  or disposition.

Reference item 8 in the below FAQ which is provided for AME guidance:


  https://www.faa.gov/about/office_org/headquarters_offices/avs/offices/aam/ame/guide/media/SubstancesAbuseDependenceFAQ.pdf


Also, according to FAA documentation, the normal look back on substance abuse is 2 years.