Depends on helmet design, my character, personal RP reasons and whether choosing to not wear the helmet impacts me severely.
Helmet design - if it's a cowl (still counts I reckon as it's the same slot), I'll almost definitely wear it as I love cowls. Otherwise, I'm likely gonna try and avoid it, though there are exceptions (Fallout: NV Ranger outfit looked pretty awesome with the gas mask - though I should say, even there, liking it, I avoided wearing it a lot of the time as I liked seeing my character's face/head).
My character - I'm more prone to not wearing a helmet if the character is female due to their hair being one of their defining characteristics for me. Also depends if it's a character I made myself or the game gave it to me. If I'm playing a fugly arse ************, I might be more prone to helmeting up.
Personal RP reasons - in some games (usually open world ones), I'm quite prone to solo RPing. In that case, I might wear a helmet sometimes and not at other times, like for example, not wearing it while going around town or wearing a certain helmet to hide my identity even when there's no such mechanic in the game or it's not impacted that way. For example, in the above-mentioned F:NV, you could wear a Ranger's body armor and as far as anyone was concerned, you were one of them. But as far as I was concerned, if they could see my face, they still knew I was me, so when I wanted to seem like a member of the NCR, I'd wear the full gett-up.
Impact - if the game has the option to hide the helmet, I have no problem doing it when I want to. When it's a matter of stats though... well it depends then, on the other factors. For Dragon Age: Origins for example, I took off my helmet and played without it through the game, because:
1) I liked my character's hair
2) Mage hats are some of the ugliest fucking things to ever grace that game with their presence
I could pull through it though. If I needed to wear it for performance reasons, I would have.