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