It depends on how long you want your vehicle to last, what condition you want it to be in when it finally dies and the experience you want to have while driving it. With something as simple as only oil and coolant changes (assuming you're also changing the oil filter), you're only considering a few components of your vehicle.
Things like the air filter, tires, spark plugs, belts, transmission fluid and filter, fuel filters, valve cover gasket, brakes, starter, battery and wipers SHOULD be changed every 12,000-50,000 miles. That doesn't mean you can't push the vehicle by not changing any of these parts for 100,000-200,000 miles. Though by doing that, you're looking at losing 3-10 mpg of gas. If you're vehicle is supposed to get 25 mpg, you're looking at getting between 15-22 mpg when the vehicle isn't maintained. Something as silly as not having your tires in the optimal air pressure range, can cost you more than 2 mpg alone.
All this being said, many of the components that should be maintained, don't have to be changed by a mechanic. Anyone with common sense, a drive to learn, cheap basic tools and at least a mechanical interest can change things like spark plugs, tires, starters, hoses, tranny fluid, ect...
And even without half of the above skills, almost anyone can change the air filter, battery and hoses by themselves.
Any car maintenance is good to learn. Not only will it save you from regular trips to the mechanic, but you can do it all on your own time. You'll also have the benefit of bonding with your car, which means you'll be more "in the know" when something seems wrong with it.
If you ever want to learn how to change certain components on your vehicle, feel free to leave a comment on my page or any of my hubs. That's what I'm here for ;)