Seatbelts always as long as the motor is running. No early removal.
No feet on the dashboard unless the shoes are off.
Lock your door when you get out.
Do you not give each other “petrol money” or an equivalent for long shared journeys in the US?
(I’m not counting own family there, obviously, as all responsibilities and expenses are shared by definition).
My only passengers are my two dogs, so my rules are:
- Stay in the back
- No barking in my ear
- No barfing anywhere
I’d like to prohibit shedding, but they’re recalcitrant on that point.
He who drives the car, drives the radio.
Passengers can sleep, eat, read, play video games, do whatever they want. Drivers gotta drive and stay awake/alert enough to do so. Therefore, the driver should choose whatever on the radio does the job of keeping them awake/alert/etc.
It might be a shared trip, but it’s not a shared experience. One person has work to do, the others don’t. And that’s the case whether or not the passenger is paying for some of the gas. If the passenger wants to listen to Kidz Bop: Swedish Death Metal, then they can bloody well drive. 
Yes, gas money is common. But it’s my style to foot the bill if the other person has less means than I do, so I control the radio. If it’s not your car, you should contribute more than just gas money too. Pay for a meal or drinks or something.
But I think the key point is that I’m driving (see my rule #1), and the driver has to get preferable treatment because he/she has to be able to pay attention to the road, stay awake, etc..
Also, if you have teenagers, they want to listen to really crappy music.
How about whacking you in the head with their tail? Blackjack is about 80 pounds, and that thing can hurt.
- No whacking me in the head with your tail
In regards to the radio thing, I’ve been known to insist on driving merely because I didn’t want to hear the others crappy music. 
Also, I’ll get there faster. 
Ya know what? If I’m making a journey, then yeah, I’ll switch off music choices with my passenger(s). It’s polite and since we’re cooped up in the car for hours on end, it makes things bearable for each of us. Plus, who knows, maybe they’ll play something that doesn’t totally suck.
But for driving to someplace in town or out to lunch or some other local destination? No. Keep your hands off my goddamn stereo.
I have fairly lax rules. Eat or drink if you want or can. I have no radio so keep yourself busy. If you want to talk to me you need to yell or I probably won’t hear you. Don’t squeeze me too tight and for my daughter and wife don’t let go. You can try and leave stuff but it won’t stay. When I am turning learn to lean. And by the way I don’t have a car, its a motorcycle.
Back when I smoked I still had smoking rules for my truck. Smoking on the highway only when no stops are likely, with the window opened at least a little. Once you stop the air is no longer getting sucked out and smoke starts oderizing the upolstery. Butts go in an empty (and capped) soda bottle (always on hand), no using the ash tray, no flicking them out the window. No smoking in the vehicle when the air conditioner was on.
Kept my truck from smelling like the typical smokers vehicle, mostly but not completely.
Yes, I followed my own rules.
I smoke, and - like you - I have a no smoking rule.
It’s not even kids related - I have none, and none have ever been in my car. To be honest, it’s smell related, and kinda pointless because no smell on earth could overcome the dog smell. But the no smoking rule is still there, even for myself while parked.
For a few years I wasn’t really able to have rules, but there were some requests:
Please try to hold it until we get there - I’m not so bad a driver as to scare the crap out of you. Even if it is your first car ride.
Screaming at me doesn’t get us there any faster.
I used to trap feral cats for a living. There’s nothing like having an angry tomcat try to spray you while driving down the road. I had a custom built vinyl lined high sided bedliner for the back of the Wrangler to avoid any of that getting on my car.
I no longer trap cats, but my Wrangler still doesn’t have a back seat. If more than one person wants to ride with me (very rare) you get to fight it out over who gets to ride in back. It’s actually quite comfy, there are usually coats and hockey jerseys back there and you can curl up for a nap.
Do not throw anything out of the window. My car is usually a bit of a mess because I do not litter.
All this fighting over shotgun, bah. Me and my sister both sat in the backseat. It’s safer for kids 12 and under anyway. And by the time we were older, we were used to both being back there.
Though I guess if you have more kids than will fit in the backseat, it might be an issue. 
Sitting up front was a treat for us - and with 5 kids, you just know that treat didn’t come all that often. This was in the bad old days when seatbelts and child safety seats were non-existent. It’s amazing we survived to adulthood.
Simple rules:
- Seatbelts
- My music
- If you make one joke or remark about women drivers (/my driving) you get out and walk. Implying things counts, eye rolling counts, sighing counts. I don’t care how far it is. I don’t care if it’s snowing. I don’t care that you were joking. This rule has been enforced several times before it was properly understood.
I don’t own a car, so when I’m driving it’s a rental vehicle. So absolutely no food of any sort is allowed. Or animals. Or smoking (although I doubt anyone would expect to be able to smoke in a car nowadays).
Seatbelts have been mandatory here since 1971, so it’s unimaginable that it would ever be an issue.
Watch for deer.
I can have the music as loud as I want. I get to sing in MY CAR and if you don’t like it drive your car. I control the radio. And don’t leave your trash in my car. I’ve got bags if you need the,
Wear your seatbelt. No messy food. Otherwise, sit down, shut up, and hold on! If you’re smoking, you’d better be on fire.