In written, formal communication, it's never wrong to use it. If you use the name, you would usually abbreviate the title:
Sehr geehrte Frau Prof. Maier,
if you don't use the name, don't abbreviate:
Sehr geehrte Frau Professor,
In oral communication in Germany, it becomes more hazy, and is subject to many subtleties. It depends extremely on context and target audience.
In my experience, most modern, young holders of academic titles are very relaxed and approachable people. It's the 21st century after all. They derive no sense of superiority from their title, and will often even refuse to be called by it, finding it ridiculous.
However, older or very class-aware individuals who see themselves elevated to a higher caste by their title may be insulted if you omit it.
It really depends on what kind of person you are dealing with, your relationship with them, and the setting.
On a very formal, high-level party to which you and your counterpart are invited in some professional function, using the title is never wrong.
In a professional setting where the person's title is relevant (say, in a hospital), older patients will usually use the title; younger ones often won't. I never call physicians by title as a patient. There is a slight risk of pissing off really stuck-up individuals though. If you are about to receive life-saving heart surgery from a snobby top-notch physician, you may feel compelled to use it. :)
In a setting that is completely unrelated to the person's title - say if Dr. Müller is a medical doctor in his mid-thirties, just came back from Africa, took some photos, and is planning to show them in a neighbourhood club setting - it's most likely safe to ignore the title and say "Herr Müller wird heute von seiner Reise erzählen".
Using the academic title is a rather subservient form of addressing someone. If used too strongly or in a context where it's not desired/needed, it will leave a slightly sycophantic impression. Much will be down to your own judgement and what is most important in your situation.
Using the academic title can also be used as a kind of gentle mockery.
Da hat der Herr Doktor aber kräftig eingeschenkt! but like with all mockery, if in inter-cultural doubt, make sure you are on safe grounds and know how much humour your counterpart is able to take.