Do "air ferries" for civilian vehicles still exist? In the 1950's and 1960's, there were vehicle (and passenger) air ferries operated by planes such as the Bristol Freighter. Mostly across the English Channel (England to France), by companies like Silver City Airways and Channel Air Bridge.  In other words, your car travelled with you on the same plane.

On that route, sea ferries (and hovercraft) eventually killed them off financially.

Do similar scheduled air ferries, for civilian cars and their passengers, still exist anywhere in the world?  If not, why?  Is the reason just financial, or are there no suitable planes any more, or did new safety or security rules make it impossible to operate them?

They would seem well suited to short hops like the Scottish islands, islands off British Columbia or Alaska, Indonesia, the Caribbean islands, and so on.  Especially in locations where the sea crossing is rough and unreliable.
There are a number of suitable airplanes - C-130 Hercules, C-17 Globemaster, C-5 Galaxy, AN-124, up to the rather monstrous An-225 Mriya. Cargo versions of airliners don't usually handle vehicles - they are designed for palletized cargo while the above cargo planes have ground-level ramps.

If you want to fly with your car somewhere it's just a matter of calling someone who owns one of these airplanes and putting down your no-limit credit card. 

As you surmised, the reasons they don't operate scheduled service is financial - boats are much cheaper, and not enough people want to go where a boat is impractical.