Depends. Do I lose out on stats if I don't wear it? If yes, I'll wear one. But if the helmet makes me look silly or stupid, I'll try to opt for a slightly weaker piece of gear that looks better. Trying to balance out aesthetics and functionality, so to speak.
For instance, in Mass Effect I always turned the helmets off, since they didn't look very good. There was no drawback to it, so why not? However, in ME2 headgear had its own stats, so I HAD to wear SOMETHING. But since many of the helmets looked silly and didn't come off for conversations, I stuck to the various visors, even though I had other pieces that had somewhat better stats.
In Oblivion, I just grabbed a black hood and slapped on the biggest Shield enchant I could find. Perfect marriage of visuals (hoods are cool) and functionality (it had 2-3 times more armor than a Deadric helmet), while at zero weight. In fact, in Oblivion you were free to wear whatever you wanted since enchants could max out your defense easily even if you wore plain clothes. And plain clothes never need repairs and are almost weightless...