Is there a way to identify what commercial airliners are still flying without ACARS today? Most modern commercial airliners are equipped, but I know some 737s still fly without ACARS, for example.
ACARS is a operator specific (optional) system. It depends on the operators requirements if an aircraft is equipped with ACARS or not. You can't tie it to an aircraft model or variant. As a rule of thumb: The older the aircraft, the less likely it is ACARS equipped.