My parents and inlaws have offered us gas money, but we've never accepted. I cant see myself asking anyone for gas money, but never say never I guess. If I was driving them around daily for months I might.
If it was something way out of the way (like an hour drive or something) then I would accept gas money. For a trip in town, no way. I drive around anyways so it's no big deal to take someone somewhere or run an errand.
I think it depends on a few things in families but no, and my MIL doesn't charge us either when she does things for us.
Sometimes I wish I could charge my son just because I get tired of being a taxi. And he's not concientious of inconveniencing me/us even though we've told him several times. (For example, yesterday when I had to go to the post office. I waited until I figured he was pretty much done. Then he called me while I was at the window to tell me he was going to stay on campus a couple more hours. I would've waited to go to the PO then.)
Naw this was a fluke request to go on a 6-7 mile-ish round trip to get a lawn mower part bc the person asking couldn't get it (had to be at work) before they closed. Not to mention all the errands this person does for his other kids and no mention of gas money to them.