Yes, always because I still hear my Dad say "you need to offer that woman your seat." However, I do have a funny story about this. Back when I was in college (so this is like 1990) and an intern for a life insurance company in Cincinnati, I had to take what I think was called "the metro" which was a city bus system. I lived about 5 or 6 miles from the office, I had to wear a suit/tie/dress shoes, etc. and I could not afford a car, even the free car my parents offered me, I couldn't afford to park/insure/fuel/maintain a vehicle so I took the bus. And I wanted a car more than anything and I hated riding the bus more than that.
Anyway, I get on the bus with 3 or 4 other people dressed for the office (suits/etc.) and I was climbing aboard last, the doors start to close, a woman jumped on right behind me, she looked like she was having herself a day. So as I'm walking down the aisle, there's ONE seat left and I would have offered the seat either way but the way that woman looked I thought "she really needs the seat more than I do." So I offer her the seat, she thanks me and about 10 seconds later she jumps up out of the seat and she said "OMG - IT"S SOAKING WET!!!"
As God is my witness, I honestly did not know the seat was wet. Of course it was a dark/navy blue fabric so you could not tell by just looking at it, but still the same, that woman absolutely wanted to gouge out my eyes. If looks could kill, they would have swept me off that bus. I apologized profusely but she wasn't having it, she was SO angry with me, the bus, the person next to the wet seat, pretty much everyone. It was pretty hilarious but at the same time I felt so awful for her, I can only imagine what the rest of her day was like.