About all any modern car needs is oil and filter every 6000 miles or
so plus lubing anything with grease fittings at the same time and
check for leaks and other fluid levels.  An automatic transmission
should get a fluid and filter change every 30K or thereabouts if you
do it the old fashioned way of dropping the pan.  Or you can let it go
to around 60K and then do a filter change but also do the flush so you
replace all the fluid instead of just the part that's in the pan.
Every 36K/3 years replace the coolant. If and when your wheels appear
to be wearing funny have the alignment checked.   Somewhere along the
way you need to have the brakes checked if you don't know how or don't
want to do it yourself.

Just make sure you do the stuff IN THE OWNERS MANUAL at the
recommended intervals to keep the warranty covered. But do NOT listen
to the dealer when he claims that the "Maintenance schedule" calls for
this that or the other thing.  Most dealers have a phony maintenance
schedule they try to get you to follow  that bears little relation to
what the car maker says is needed.  It will have things like "injector
cleaner" and "brake cleaning" and other crap like that which is just a
way for them to make large profit margins on unneeded work.
--
Elbridge Gerry, of Massachusetts:

"What, sir, is the use of militia?  It is to prevent the
establishment of a standing army, the bane of liberty.  . .
Whenever Government means to invade the rights and liberties of
the people, they always attempt to destroy the militia, in order
to raise a standing army upon its ruins."  -- Debate, U.S.  House
of Representatives, August 17, 1789  

"Running fine" is irrelevant.  A car will run fine for quite a while
without oil changes.  Maintenance means doing service before parts
start breaking.

I've always trusted the manufacturer's owner's manual over the
"experts" selling service at the dealership, or Internet experts like
me.

True story:

On my last car, I got a computerized post card from the dealer where I
bought the car telling me I was due for an automatic transmission
fluid flush.

Just for fun, I went in, played dumb, asked if it was really
necessary, had the service manager write it up, and the mechanic was
in the car ready to drive it in for the "flush" before I stopped him.

The car was a manual.  The only thing they were flushing was money out
of wallets.