You need to change your oil every 3,000 miles: This used to be true for older cars, but modern engines and oils can last much longer. Most manufacturers recommend changing oil every 5,000 to 7,500 miles, and some can go as long as 10,000 miles between oil changes.
Premium gas is always better for your car than regular: This is only true if your car specifically requires premium gas. If not, using premium won't provide any benefit and will just cost you more money.
You should idle your car to warm it up before driving in cold weather: This used to be necessary for older cars, but modern engines are designed to be driven right away, even in cold weather. Idling your car just wastes gas and creates unnecessary pollution.
All-wheel drive or four-wheel drive means you don't need to worry about winter tires: While all-wheel or four-wheel drive can help with traction, they don't provide any better braking performance on icy roads. Winter tires are specifically designed for cold weather and provide much better grip than all-season or summer tires.
You should replace all four tires at the same time: If only one or two tires are worn out or damaged, you don't necessarily need to replace all four. However, it's important to keep the same type and size of tire on each axle to maintain proper handling and stability.

You should always follow the tire pressure listed on the sidewall of the tire: The tire pressure listed on the sidewall is the maximum pressure the tire can handle, not necessarily the recommended pressure for your car. The recommended pressure can usually be found in your car's owner's manual or on a sticker in the doorjamb.
You need to change your engine air filter every 3,000 miles: Most cars only need their air filter changed every 15,000 to 30,000 miles. However, if you frequently drive on dirt roads or in dusty conditions, you may need to change it more often.
You should change your transmission fluid every 30,000 miles: While this used to be true, many modern cars have transmissions that are designed to be "lifetime" fluid, meaning they never need to be changed. Check your owner's manual for the manufacturer's recommendations.
You need to warm up your engine before driving after it's been sitting for a while: Like myth #3, this used to be necessary for older cars, but modern engines can be driven right away. However, it's still a good idea to drive gently for the first few minutes to allow the engine to warm up and the oil to circulate.
Using a higher viscosity oil will always provide better engine protection: While higher viscosity oil may provide better protection in extreme conditions, using it in a car that doesn't need it can cause unnecessary wear and tear on the engine. Always use the oil viscosity recommended by the manufacturer.