Do your own inspection. Before getting on any rides take a look around and size up the park. Is it clean and well maintained? Inattention to maintenance in general may indicate inattention to the rides. Do the ride operators seem professional and competent, and are they paying more attention to the ride they're operating or to the people walking by?
Watch the rides in operation. Rides should look and sound like they're in top condition and run smoothly every time. Look out for rust, cracks, and jerry rigged repairs. The more you know about how the ride should operate, the better. A little sway in a wooden roller coaster framework is not only expected, it's built in. The same sway in a steel track could be trouble.
Check your own restraints Buckle any seatbelt, make sure your lap bar or "horsecollar" (over the shoulder restraint) locks down, visually inspect pins and door latches. If you find a problem that the ride operator missed, speak up-- so it can be fixed before you ride.
Keep hands and arms inside the car at all times. We hear the warnings so many times we no longer pay any attention, they become so much background noise along with the rumble of the wheels and screams of delighted riders. Take the time to listen to all warnings and instructions -- and follow them. Stay seated, and keep all body parts you want to keep inside ride vehicles and away from tracks and machinery.
You must be this tall. Don't argue with the ride operator because Junior is too short to ride -- he or she didn't set the height limit and must follow it. Restrictions are based on the size and position of the ride's restraint system, not some sort of anti-child discrimination. It's better for your child to not ride and be disappointed than to slip from the ride and suffer an injury that could last a lifetime -- or end it.
Respect all posted ride restrictions. Some rides restrict pregnant women and persons with back problems, heart conditions, etc.. These are usually rides which involve sharp, sudden movements or a great deal of shaking about and may even be quite a workout for the perfectly healthy. Don't assume that the park is exaggerating the danger; there are a few tragic cases of children with known heart problems collapsing after riding attractions that have served millions of satisfied healthy riders safely. There's no way a ride operator can check for such hidden problems, if you know of a reason why you or your child shouldn't ride, don't ride.
Do not stand up on roller coasters or other rides. Those signs at the top of the lift hill are there for a reason -- standing on a sit-down coaster puts your center of gravity much too high, and the same forces that ordinarily conspire to keep you in your seat now work to throw you from the train. Too many people have died this way already, do not push your luck. (Obviously, coasters which are designed to be ridden standing are an exception.)
Don't rock the boat, or the log or the vehicle or the seat of any ride. Let the ride provide the motion -- attempts to jazz up a ride by rocking or swinging can cause the ride to jam or shut down and you could get hurt in the process. Tramway type cars cars are subject to having their cable slip the guides, in which case you'll be stuck up there, or having the car slip the cable, in which case you'll be hitting the ground very suddenly. Even the ordinarily safe Ferris wheel can turn deadly if the seat is rocked high enough to spill its passengers. If you absolutely have to have an effect on your ride, try a ride that is designed to shake you up.
Report problems to the park or carnival. If you do notice an unsafe condition or see someone doing something foolish, notify a ride operator or guest services. After all, they can't fix what they may not know about. Wouldn't you rather feel embarrassed over a misunderstanding something than feel guilty because an accident was about to happen and you failed to stop it.