The best-known and most typical was Mycin. See e.g. Winston Artificial Intelligence 3rd ed, pp 130-131. Also Goodall pp 16-20. Its job was to diagnose blood infections and recommend treatments, given lab data about tests on cultures taken from the patient, etc.
One of the earliest expert systems was Dendral, described on page 51 of Winston. It was designed to analyse mass spectra. For the purpose of this description, a mass spectrum is a particular trace or analytical record formed when a molecule is bombarded with electrons. Each molecule has its own spectrum, determined by the way it breaks into fragments when hit. Chemists have charts of mass spectra for some common molecules. And they know some general rules that determine how a given type of molecule will break up, and what kind of spectrum it will give. But identifying a new molecule from its spectrum is not easy.
Be warned. Dendral did contain rules, but it worked differently from most expert systems. Mycin is more typical.
And the two literature examples of commercially exciting systems you'll always find are Prospector and XCON/R1. Mycin has never been used for real diagnosis, perhaps partly because of fears over who'd be legally responsible for mistakes; Dendral was used by many chemists at Stanford, but probably never outside acadamia.
Prospector took geological information about rock formations, chemical content, etc, and advised on whether there were likely to be exploitable mineral deposits nearby. Popular accounts of AI say that Prospector (in 1978-ish) discovered a hundred-million-dollar deposit of molybdenum. Certainly, this ``fact'' helped raise business interest in expert systems. But the deposit was never exploited: I don't know the details, but it may be that Prospector mis-advised on the value or ease of extraction of this deposit.
XCON is described in Winston p 139. It is often mentioned because it was one of the most successful expert systems: it performed a task that couldn't be done manually or with a conventional computer program. It helped ``configure'' computer systems for DEC (who make VAXes amongst other things). See Crevier pp 161-162 for a summary, and for the origin of one of its names. (``I always wanted to be a (knowledge) engineer, and now I are one''.)
Summary of configuration problem: When you buy a big computer, you need to order lots of parts: processor, power supplies, cables, discs, memory, etc. All this must be wired up sensibly, and arranged in the right kind of cabinet. For any set of parts, there are many ways to do this; complicated by the vast number of similar but not identical discs, memories etc that DEC sell. DEC were finding that their customers made mistakes in ordering; technicians failed to catch these errors, and made mistakes themselves in designing the configuration; so they decided to design a program to do it. XCON took about 3 years to get right, but it eventually handled, according to one writer, most (90passing those it can't cope with to a human configurer. DEC said it had saved them significant quantities of cash. However, see also Crevier p 204. The joke was that XCON may have replaced 75 people, but 150 were needed to keep it running.