Head armor is one of the safest places to take off armor from. It is incredibly hard to hit if the target is moving and it is only susceptible to high powered projectiles like AC20 and Gauss. I take off as much as I can, sometimes dropping as low as 6-4. Some mechs like Battlemaster have a slightly bigger head that gets headshotted slightly more, especially to artillery but even full head armor doesn't save you from that anyway.
Leg armor is slightly more complicated. For lights, full leg armor is obligatory since they're extremely easy to leg. Especially mechs with long legs like Ravens, Firestarters, Locusts and Spiders should never drop without full leg armor.
For others, it depends on if the mech is jumpjet capable. Jumpjet mechs have the advantage of "leg tanking" when they're in the air, especially close range jumpjet brawlers that I tend to run. So, always drop with full leg armor when using a JJ mech.
My non-JJ mediums also usually have full leg armor, since they're usually fast and tend to get a lot in the legs as a result(especially LRM's hit your legs more when you're on the move). Not to mention lights love to leg mediums, since they're incredibly easy to take out when you take the ability to "speed tank" from them.
Non-JJ heavy and assault mechs always get some leg armor shaved off, since 90% of the time you're easier to take out in the upper torso. Still, depending on your tonnage a decent leg armor is needed, because they need to hold until your torso armor opens. If your leg armor is gone before your torso, somebody in their right mind WILL leg you and dictate their mobility while you suffer. I found that 40-50 is good for most heavies and 40-60 for assaults.
Though, when you're in the heavy-assault brackets, the mech you're in also makes a lot of difference. I dropped to as low as 33 in my Orions since their upper torsos are so squishy, people tend to focus on them first. If you don't get showered by LRM's, you will be just fine. Same goes for the Awesomes, their upper torso is always targeted first. My Awesomes used as low as 37 leg armor when I needed the tonnage.
When you move towards 100 tons though, you need to considerably beef up your leg armor. A Stalker is an incredibly tough nut to crack for lights and mediums at close range and for others at medium-long range. So, a frustrated light will more than likely tap your legs to see if you've made that "fatal mistake". Almost all my Stalker kills are due to legs these days, thanks to those LRM boats. A Battlemaster should also have beefier leg armors since it has such colossal, long legs that tend to get hit a lot. Atlases should never drop below 60 in my experience.
I think this mostly comes down to preference and the type of role you're playing. A lot of long-range support pilots completely strip their unused arm armors to make tonnage, which is fine. I run mostly brawlers and torso twist rigorously, so I usually have full arm armor to add more survivability.
Again, not all mechs are created equal though. A Trebuchet will often get its arms shot off and most hardpoints being on arms, they should never take armor off of them. Same goes to Dragons, Centurions, Catapults(missile variants), Victors and so on. The opposite is also true, it's incredibly hard to lose an arm in Orion since they're so skinny. Cataphracts, oddly, also don't lose their arms much. I dropped my arm armor as low as to 20's in my Orion and still not lost them in many matches. If you know your mech and believe it can do with lower armor, you can mostly get away with it.
Full armor is usually the norm, except in mechs with extremely bad hitboxes(like the Trebuchet). I played well above 600 matches in my Trebuchets, and I can probably count the times I died to a ST destruction with my fingers. I successfully shaved off about 10 points from my Treb ST's and didn't notice a difference and as I said, I consider my twisting to be pretty good.
The distribution is the king here. The rear armor is the real problem, so my values are always for rear armor. For my lights-mediums, I never drop below 10 rear armor, even in lights. You should have enough armor to survive an AC20 to the rear, without screwing your CT/ST internals. After that, it's up to how that mech performs. My normal distribution is 12-15CT, and 10ST's.
Heavies usually need a little bit more, but not much since they still have decent mobility to protect their rear. I have about 15-18CT and 12-14ST rear armor in them.
For my Assaults, it's obviously more. In brawls you won't be able to control where you take damage from. My Assaults usually sport ~20CT and 14-16ST armor, enough to survive two alphas from most mechs. My Atlas is the real juggernaut with about 25CT and 20ST armor. It also allows you to tank with your rear if your front is screwed up.
Again, some mechs can get away with less and some more. Some mechs have to break the rules and have more ST armor, like Orions(I keep giving it as an example, but hitbox-wise this is a truly unique mech).