How important is it to get the recomended routine maint. checks on a care. IE - the checks that are recommended periodically at different milage.
Very important if it’s recommended in the owner’s manual.
Very expensive if it’s recommended by the dealer but not the owner’s manual.
And ultimately, even more expensive when failure to check certain vital items leads to repairs that could have been prevented!
Check the oil, coolant, brake fluid, and power steering fluid levels yourself. Your owner’s manual will tell you how often they need to be inspected/changed.
Whoever changes your oil should also check the car’s vitals while it’s in there (belts, hoses, fluids, etc).
Yes it’s important only if it’s recommended in the owner’s manual.
Coolchick; many of these routine checks you can do yourself. As others point out, not doing them can lead to expensive and unnecessary failures. Car care is a lot like dental and health care. Regular checkups are essential.
I would first read the owner’s amnual; it usually has a list of things you should check yourself, such as tire pressure, oil level, coolant level, etc. Some one can show you how to do this if you don’t know already.
Other items listed in the manual will require a mechanic to do; those you should trust to a good technician to do these. I would ignore items the dealer suggests or tries to scare you into doing, if they are NOT IN THE MANUAL.
If you want a car to last and be reliable, doing routine maintenance, as specified in the owner’s manual, is absolutely essential. This is true regardless of the make, model, year, or mileage of your car.
Saving money by scrimping on, or skipping, maintenance is false economy, and will end up costing you more in repairs later.
You don’t need to do extra things, which dealerships and some mechanics will try to sell you, but you DO need to follow the schedule that came with the car.
Is this issue a discussion item somewhere? Is someone advising you that following the recomended maint. checks are of no value?
Now if the issue is cost, you can learn and set yourself up to do all checks yourself
There is the “run them until they die crowd”.
One option is to not only perform the ones recommended in the owners manual (it’s in the glove box) but in regards to some items and some cars there are a few areas that should be serviced more often that what the manual states.
The owners manual is not always the final word if one REALLY cares about their car’s well-being for the simple reason that many car makers want you to believe that their cars need very little maintenance. Therefore, they “stretch” some recommendations and by the time a problem occurs due to this “stretching” the warranty will likely have been up and you’re on your own; while also being ohlivous to the fact that THEIR chintzy recommendations are what led to YOUR problems.
The other option is to do like many others do; drive it while doing as little as possible then become totally puzzled when a transmission drops, cylinder head valve problems occur, fuel pumps quit, etc, etc, etc, etc, etc.
Off the soapbox now. 
We all like to save money. You can save the most be learning how and doing it yourself. You also know it was done right. Next best bet is to find a good local INDEPENDENT mechanic, they are just as good or better than the dealer and charge less most of the time.
The worse thing you can do is to bring your car into a national chain like the quick oil change places and national department store auto departments. They live by selling things you don’t need and often make mistakes that damage the cars they work on.