No routine medical as such, but there are medical requirements for car drivers and should there be ambiguity about whether or not you meet them... a medical.
Personally speaking I have mixed feelings about it. I suspect the medical is overkill for most, but then how else do you ensure a ready supply of medical professionals who understand aviation and can advise when required? I'm not sure that the risks are as low as all that.
1) psychiatric - suicide by light aircraft is not all that uncommon.
2) medical - an epileptic seizure or collapse in a car is more likely to hurt a bystander; in an aircraft it's likely to prove fatal to the pilot and any occupants.
3) sensory - good sight and vision are quite important
4) general wellbeing - the number 1 cause of accidents is stupidity. We're more likely to be stupid when we're under the weather.
Stereotypical incapacitation accidents are probably quite uncommon, but a 'medical' contribution to aviation incidents is probably much more widespread.