It all depends on the driver. With most people I’m fine, there are others however who have terrified me. Even with these drivers I will not usually say anything at the time, I’ll just never get into a car with them again.
I prefer to drive and of course, nobody can drive as well as I can. 
Mr. Adoptamom and kidlets went to dinner tonight with our elderly next door neighbors. Mr. Neighbor, 75+ yrs old, drove. The ride there was uneventful. The ride home was quite a different story as it seems Mr. Neighbor turned onto a two lane road believing it was a major city 4 lane highway and he was on “his side” of the median. Did I mention the two lane road has very deep ditches?
Mr. Adoptamom told Mr. Neighbor that if I’d gone with them tonight, as originally planned, that I would’ve killed him quickly and mercifully, after I’d ripped the headliner from the car, the handles off the door, and the dash out of place. 
I’m glad I asked for a doggy bag
that is exactly how it is for me too. There is slightly less chance I won’t throw up if I am in the front passenger seat, but…travel sickness aside, on the rare times I am a passenger, I get way too nervous. I know what caused it, so it’s not quite so bad, but even so. *shudder.
I generally am a pretty nervous passenger. Once a group of us went out for lunch and one of the young guys in the office gave 4 of us a lift. He was (probably still is) a terrible and terrifying driver. On the way back he ran a Stop sign and when he pulled up at the lights I got out of the car and walked back to work.
When my son was learning to drive I adopted the approach used by TheLoadedDog. I thought it was important to remain very calm and would often feign indifference while really watching everything. The experience has made me more able to ignore things.
For me, it depends on what car we happen to be in and who happens to be driving. I’m more nervous if my brother is driving my car than if he’s driving his own. I made rules for him illustrating which things would be acceptable, and those that would not be acceptable. When he does something that makes me nervous, I hold my breath. Then he looks at me funny because he knows I’m not breathing.
I absolutely cannot tolerate my sister’s driving in any vehicle. She’s just awful. She sits way too close to the steering column*, thus sitting too close to the airbag for my own personal comfort. She accelerates too slow, she makes turns too fast, and she doesn’t adjust her pressure on the gas when she’s going up (or down) a hill. She won’t leave a stop sign until she’s absolutely sure it’s 100% okay. I’m always saying, “Hey, you could have gone like six times just now”. I think something may be wrong with her depth perception. Sure, caution is good, but that’s ridiculous.
I agree with Airman though. Do not scream or alarm me in any way while I drive, unless there is an imminent danger and I’ve somehow managed to completely miss it. Scaring the hell out of me because you didn’t like the way I merged onto the freeway is the surest way to get my foot in your ass.
*This isn’t because she can’t reach the pedals any other way, either. She’s not that much shorter than I am and I’m very cramped in the driver’s seat of her car. My mom does the same thing even though I tell her all the time that it isn’t the safest place for her to be.
My fiancee and I are each active passengers, but we also respect the “don’t shout at the driver” rule. If there’s danger, we alert each other to it in a generally calm voice, e.g. “Red light” or “on your left.” When the driver signals a right-side lane change, the passenger checks the blind spot and says “clear right” so the driver can keep eyes front. Constructive comments (“You’re following a little close” and “that asshole at your 10 o’clock is going to merge without signalling any second now”) are always welcome, and we both holler in unison “GO YOU FUCKER, GO!” when someone passes us at Warp Nine because they’re In A Real Hurry ™. This is in the hopes that he or she will help fund our local constabulary and possibly get his or her license suspended. We also both creatively curse poor drivers.
In short, I’m an active passenger, and so is she. We both watch the road all the time. This may or may not stem from driving in D.C., but it certainly has saved us more than once.