The full model number (visible on the placard below the fridge or inside the fridge, freezer, or door on the label, which will have the full model number beginning with three numbers followed by a dot. Those three numbers will tell you who manufactured it. Then check their reliability in old issues of Consumer Reports from about 4 years later. Also check Epinions, Amazon and the like for reviews on similar models from that manufacturer.

I have never found a "good" site with reviews on used appliances. I do not think anybody maintains such a site, anyway. Searches for that turn up only shopping redirection sites and sellers of used appliances where the reviews are only about what great guys the vendors are. You have to go back to "vintage" appliances to find anything like you are asking about.

As lee76 says, you are better off just running searches on the fridge model number. You may find reviews of what people thought of it when it was being sold. Consumer Reports --- you will have to go to a library to find old print copies.CR's online archives only go back about 4 years or so.

A search also will turn postings on various sites like fixya where people have had problems and are trying to fix the unit. That may at least tell you something about what goes wrong with the unit and how hard it is to locate the parts.

Many charities do not accept appliance donations over 11 years old because repairs are not feasible.
Moving/Transporting old refrigerators without taking needed protective measures can result in failure at the new location in a relatively short time.

Just wanted to take a moment to thank you all for your replies. It's great to know there are some nice people who are willing to help.

All of my appliances are old and I am looking to replace them with good used appliances. As you know the problem is not all appliances are equal and there are some lemons. It would be very helpful to have a free website aid shoppers.

Thanks again for your aid.