I have no intention of charging anyone for gas, and just want to understand the rules better. So let me throw a few scenarios at all of you:
Scenario 1
My daughter wants to go to San Diego and stay for a week. I offer to fly her, so that I can make my first IFR flight to San Diego IFR for the first time, and shoot an approach into KSAN. I will drop her off and depart within the hour. We both "want" to go to San Diego, but not for the same reasons, and it wasn't "my" idea to go. Furthermore, I likely would not fly to San Diego solo just for the experience, but she doesn't want to drive, so I decide I "want" to go.
-No
Scenario 2:
Same as above, but I decide that my official "mission" will be to visit some dinner I saw on "Diners, Drive-ins, and Dives", before returning home. Again, I likely would not make the trip had she not said she wanted to go to San Diego.
No
Scenario 3:
My wife wants to go to a mega-mall in some city an hour's flight away. I have no interest in going, but she doesn't want to drive. I don't have the money for the trip in my "flying budget", so she says we can afford to pay for the gas out of the household budget, because we didn't go out to eat so many times this month. The flight was not my idea, and I wouldn't be flying to that city on my own, and if she cancels, I'm not going.
Yes, effectively you and your wife are one person (shared money)
Scenario 4:
I fly to Monterey at least a few times per month for various reasons. (A 1hr hop.) To go to my favorite eateries; to visit friends; for doctor's appointments; and sometimes just to shoot approaches in IMC. A friend knows I make these flights, and says he wants to tag along, and be dropped off to visit family. (He will find his own way back.) It would be "my" idea to go, and will be going whether he goes or not.
Yes
Scenario 5:
A friend and his wife want to go to Half Moon Bay for lunch at a restaurant within walking distance of the airport. They know that I fly there to eat on occasion, and ask if I am going anytime soon. I have no immediate plans to do so, but am more than willing to go any day they like. They pick a day, and I decide, "Hey, I want to go to Half Moon Bay for lunch," on that same day. Since it is close by (unlike San Diego) I would likely go even if they cancelled. But it was not originally "my" idea to go on "that" particular day.
Probably not
Conclusion?
It seems like maybe the FAA's idea of "common purpose" is "It was my idea to go" or "I was already planning on going", AND "I would go with or without the other party." Both are gray areas that I don't think I would want to venture into unless I REALLY trusted my passengers not to rat me out. (And I don't trust ANYONE that much.)