Yes, always do!
It's not supplicating as Superman said ... this is another part of the decline of the American Male. They're clueless in how to handle themselves in front of women.
While I've posted often on the p-ssification of American men, being CLASSY is not AFC, it is the right thing to do, period. Women LOVE it when men open doors for them and all alpha (real men) open doors for women. They're not worried about what the woman thinks and they don't think it's supplicating them.
I open lots of doors for women all day, cute, homely, fat, thin, just right, all kinds of women. I open the door and smile and ALWAYS get a thank you, smile.
Have we gotten so hardened and bitter that we can't give a nice gesture. And didn't your dad's teach you right? Superman, you are definitely NOT superman but a weak man who is so worried about what women think of you that you in turn are weak.
Be confident, be strong, be ****y, be confident. If a woman can't handle a nice gesture then she's not the one for you.
I'm amazed at some of these posts.