I put the "developed world" declaimer as I figured in some poor countries you wouldn't be able to get good treatment without paying for it but I imagine even then you will not pay as much as in the US.
Generally free or not available at all to that specific patient, no? At least from the publicly funded system; some Western European countries also allow private practice of medicine where the availability criteria are different.
If it's a treatment that is required for the patient to survive it will generally be available & free. E.g. getting cancer treatments here will be free & almost certainly expensive in the US (even with insurance they will find something the insurance doesn't cover, and/or will charge you for stuff like ambulance rides).
There may be some rare exceptions where you'd be able to pay a lot of money in the US for some experimental treatment not yet available in the public EU system but this is the exception not the rule. What you possibly won't get for free are non-critical treatments.
I will give one declaimer though that I live in Germany & the healthcare system is not in the same quality/extensiveness throughout the EU (the German system is among the best).
In Western Europe such things are generally free.