Oil/Oil Filter Change
Changing the oil should be the most frequent part of your car maintenance, and should occur every 3,000 miles or 3 months. If you're using synthetic oil, then you can perhaps wait 5,000 miles or 6 months. Change oil filter as directed by the owner's manual.
As needed, or according to manufacturer's recommendations.
Your front tires and back tires experience different rates of wear on different parts of the treads. By properly rotating them every 5,000-8,000 miles, you can uniformly disperse the wear across your tires. Also maintain proper tire pressure.
Dirty spark plugs can adversely affect gas mileage. Your owner's manual should state when your spark plugs need to be changed. Depending on the type of spark plug you're using, it can be anywhere between 30,000 and 60,000 miles.
An inspection of your timing belt should be done every 10,000 miles although if nothing is wrong with it, it doesn't have to be changed. Minor spider cracks on the surface of the belt are okay, but if a visual scan reveals severe cracks or broken teeth, then its time for a new belt. Failure to do so can result in hefty damages. This should also be changed at the manufacturer's recommended mileage.
Windshield wipers should be replaced at least twice a year. They're cheap and easy to do yourself.
Everything from the pads, to brake rotors, to the brake fluid should be monitored. There is no set mile limit as to when the brake pad might need replacing. It is largely affected by your individual driving style (how hard you brake and how frequently), and can be anywhere between 20,000 to 40,000 miles. Brake fluid should always be at the appropriate level, and is an easy check around the back of your engine bay. If it looks dirty, or for whatever reason is too low, then it's time for a refill.
Power Steering Fluid
Similar to brake fluid, power steering fluid can be visually monitored from the engine bay. If it's dirty or low, then it should be refilled.
This keeps your transmission lubricated and happy while preventing corrosion and rust. Most manufacturers will recommend changing the transmission fluid once every 30,000 to 60,000 miles. Consult your owner's manual to be certain for your car. If the auto shifting in your car isn't as smooth as it should be, that is also a good indicator to have a maintenance check. There are many more parts of car maintenance (battery, wheel bolts, coolant, fuel filters, the PCV valve, and the electrical components) that are absolutely essential. All of them are necessary in the long term. Learning how to do most of this yourself can save you money as well as time.