Do you iron your underwear?

No. I never seen people ironing their underwear. That is only a waste of power. For a small clothing that people can't see it.

i don't know, my guess is they are probably a little paranoid so they think they have to iron everything?? do they iron socks too?

I do...only when it is still wet, not dried completely after a wash or something and i am in an urgency to wear it, when i am away from home where i carry only one or two underwears, other than that may be people iron it to keep it wrinkle free and neat

Normally, I don't iron my under wears. However, during the rainy season, drying up laundry is quite difficult. That is the time I do iron my under wears. Especially if I already need one and the clothes are still not dried yet. Also, when doing the laundry sometimes, the clothes are left hanging outside overnight. The evening breeze and morning dew dampens the clothes. That is the time I will iron too. But if the under wear is perfectly dry, I wouldn't bother to iron it.

No, I have never even thought about ironing my underwear. I don't really see a need to do so because, as you said, nobody is going to see it anyway. The way that I see it, if other people see my underwear then I will be so embarrassed that it won't even occur to me that they were wrinkled.