I was taught to do this and still do it to this day. It's disheartening when there are those, though, who don't even bother to acknowledge the gesture with a simple, "Thank you." One time, however, a woman really pushed me over the edge.
I was walking into the mall one day. As I usually do, I glanced back to see if anyone was coming behind me. I saw that an older woman was coming, so I paused and held the door open for her. She walked up to me, stopped, and said, "Young man! I am quite capable of opening my own doors!" For some reason, that sort of insult really burned me. So, I replied, "Fine!" I walked through the door and let it close in her face. When I got inside, I again glanced back to see the woman still standing then both angry and confused.
I don't hold the door open for women because they aren't capable. I do it as a sign of respect. As I sometimes tell my wife, "It's not that you can't do it. It's that you don't have to do it."