Reading this question, there are many good answers to why stormtroopers don't remove their helmets.
Despite all the reasons given, he clone troopers do. Why ?
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whom do we actually see remove their helmets clone wise in canon? Obivously, the clone CT-5555 "Fives" and some others do it in the clone wars season - but in the movies I can only recall unhelmet clones at two occasions:
(1) in the training facility on Kamino as childs or whilst eating at the cantina.
(2) CC-2224 during a meeting with Obi-Wan Kenobi, I assume this was for better understanding purposes. Obivously, given the fact CC-2224 was a clone commander MARSHALL, who had command of over 35.000 clones, it seems to be in his full authority to remove his helmet when he pleases to do so.
Clones where designed to follow any order without a doubt, but else had the freedom to finish their assignment by any means they saw fit that were within' their parameters. This set them apart from the droids in a good way as mentioned by Lama Su in EPII:
LAMA SU:They're immensely superior to droids, capable of independent thought and action.
OBI-WAN: Very impressive.
LAMA SU: I'd hoped you would be pleased.
On the other hand, I found a reference as to why Stormtroopers wouldn't do so if not absolutely necessary from EPVII:
CAPTAIN PHASMA: FN-2187. Submit your blaster for inspection.
FN-2187: Yes, Captain.
CAPTAIN PHASMA: And who gave you permission to remove that helmet?
FN-2187: I'm sorry, Captain.
CAPTAIN PHASMA: Report to my division at once.
Part of the reason why the military and other organizations adopt uniforms is depersonalization. If everyone is wearing the same outfit, it creates a sense of interchangeability, that every person is a cog in the machine, ready to substitute if one of them should fall. If someone beside you is shot, you step into their place in the ranks instead of stopping to check on Bob, the guy who collects plastic unicorns as a hobby.
The clones were raised (and seemingly programmed) for obedience and a lack of self-identity, so there's no risk of individuality, but the stormtroopers are humanoid recruits, so the regulations likely require wearing of helmets at all times, ostensibly for the purpose of safety (compromise of environmental conditions, rogue Rebel sniper) but moreso because it keeps the stormtroopers thinking of each other as units, not as individuals.
Glancing over, it looks like this answer to the other question discusses the depersonalization in stormtroopers to a greater extent.
I think there are obvious production differences. In the films (IV - VII) storm troopers are baddies, we want them dehumanized. Where as in the films II and most of III they are characters we are meant to relate to and empathize with. With the clone wars this is especially the case.
There is also the issue of individualism. Storm troopers are not clones (or at least not in known cannon). So there is an effort to make them more uniform. Clones are uniform with or without a helmet (baring hairstyle, and scars) so there is less impact in removing it.
The Imperial armed forces the audience of the movies see is divided into Ranking Officers of the Imperial Navy, and Stormtroopers.
The Clone Army only has clones, some of which are high ranked, but still wear armour.
There is a pretty well established trope that sergeants, commanders and heroes do not wear helmets.
http://tvtropes.org/pmwiki/pmwiki.php/Main/HelmetsAreHardlyHeroic http://www.dakkadakka.com/dakkaforum/posts/list/447814.page (Warhammer 40k) https://www.reddit.com/r/HaloStory/comments/3ku63f/how_come_sergeant_in_the_unsc_marines_dont_wear/ (Halo)
So the answer is, none of the Stormtroopers we see in the movies are important enough in the plot, or high ranking enough to fit into the trope of not wearing helmets. There's no need for the audience to be able to tell them apart. There are plenty of ranking officers in the Imperial Navy that don't wear a helmet, they just don't wear body armour either.
Clones not wearing a helmet are those that meet the TV trope. The audience needs to recognise them.