Shiny planes
 

Most aircraft I have got close to seem pretty clean generally.

So I suppose they must go through a car wash from time to time.

But do they they get waxed to make them really slippery to save fuel?:8

Yes, particularly carriers like American Airlines who have very little paint in their livery, most of the aircraft is just unpainted aluminium.

Wax is not used, but they perform regular polishing, or "buffing", of the exterior unpainted panels to maintain the bright finish, and in fact calculate it costs them more to do this than to maintain paintwork in good condition. There is an assessment that dirty exterior aircraft add to drag and thus fuel costs.

The "car wash" is done from time to time on all aircraft, often in front of the maintenance hangar. Demineralised water is used, another substantial expense in the process. One of the worst items for accumulating dirt is the sticky residue from de-icing operations, so carriers like Finnair with a lot of heavy winter operation have extra cleaning work to handle this.

Air France is renowned for a white livery, infrequent washing, and filthy exterior aircraft. Possibly aircraft washers are expensive and fuel is cheap in Paris ? :)