Painting of aircraft and the levity allowed for individual markings depended on the time, place, air service doctrine and conditions.
For example Royal Air Force and Germany-based Luftwaffe aircraft tended to be painted in the standard schemes proscribed by the high command. Individual markings such as crests, cartoons or victory markings were either discreet, or were a privilege of success or seniority. The VVS (Soviet Air Force) allowed, indeed often encouraged, patriot slogans but again individual markings were relatively rare.
The USAAF took a somewhat more relaxed attitude, especially for its forces based in England (and therefore at some distance from the 'top brass'). Their commanders were often young officers who led with flying skill and charisma, and individual markings proliferated. A key reason for this was that for most of its time, the 8th and 9th Air Forces in England were dominant and aggressive: they had little reason to hide and this is why we see the late-war fleets of B-17s and B-24s flying in natural metal finish. The Allies by this time had such a huge advantage in numbers, training, and equipment that they could dare the Luftwaffe to come at them.
Proving the rule, as the Luftwaffe came to be hunted on the ground and in the air in 1944, as the only viable combat tactic was to hit and run, their aircraft became darker, more drab, and with few individual markings. Interestingly, this is pretty much the reverse of the situation in 1940 when Royal Air Force aircraft, fighters and bombers, were painted brown and green for camouflage on the ground, while the Luftwaffe's Messerschmitts had sky blue sides and bellies, for better camouflage in the air.
As the Royal Air Force moved into an offensive posture in 1941-2, it's fighter scheme became grey and green, for better camouflage over water and in clouds. Other schemes were developed for night bombers, coastal patrol and attack aircraft, night fighters (which, it was proved, needed a different scheme to night bombers!), and desert-based aircraft. The intense fighting over the Mediterranean island of Malta saw local colour schemes applied emphasising blue to blend in with the turquoise waters, a rare case of prolific use of non-standard paint in the RAF. A similar situation applied to parts of the Eastern Front, where the Luftwaffe's Jagdgeschwader 54 used captured paint to camouflage its aircraft in summer, 1942.
A significant minority of RAF night bombers received individual markings. My father's Lancaster had two distinct nose art pieces at different times, one in chalk and one in paint. The original was overpainted when the aircraft was given a major service.
The US Navy had a very different attitude to the Army, and individual markings were very rare and very small. A fighter squadron that applied a 'cat's teeth' marking to its F6Fs was ordered to overpaint the markings. This was an example of service culture rather than tactical considerations.
A final issue is the schemes needed to be simple: early in the war the USAAF experimented with some very elaborate colour schemes intended to deceive an attacker as to his 'victim's' distance, direction and attitude, like naval 'dazzle' schemes. While they worked very well, it was found not worth the effort to paint on the intricate patterns.
Some people reading this will be able to cite examples that seemingly prove how planes could be painted any which way, but it is worth remembering that unusual schemes tended to attract photographers!
Fighter Colours Michael Bowyer. Bomber Colours Michael Bowyer. Soviet Air Force Fighter Colours, 1941-45 Erik Pilawskii