The following applies to US English, which I assume is the context of your question.

*Customers* is typically used when the commercial interaction: 1.) Involves the purchase of goods; and 2.) Involves the purchase of services that are not considered professional in nature.

Thus, under #1:

Customers of a department store.
Customers of a gas station.
Customers of a bank.

And under #2:

Customers of an oil change center.
The customers of a dry cleaning store.

"Clients," on the other hand, is mainly used in reference to services considered more "professional" or "involving" (i.e., in terms of the relationship between the provider and the purchaser) in nature. (Of course, in medical or para-medical contexts, "patients" would generally be used rather than "clients".

Thus:

The social worker's clients.
The psychotherapit's clients.
The clients of the weight-loss center.
The hairdresser's clients.
The stockbroker's clients.
The insurance broker's clients.


I am sure that exceptions to this general rule can be found, but this does seem to be the general rule (again, for US English).

Suerte.

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Note added at 23 mins (2010-09-16 19:27:43 GMT)
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Typo:
"psychotherapist's"

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Note added at 1 day16 hrs (2010-09-18 11:49:37 GMT)
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A mi juicio, si no se se sabe en concreto a que circunstancia se refiere, la mejor opcion es usar la palabra "customer" en ingles. Pero si se se sabe a la relacion a la que se refiere, se puede usar mi explicacion como una pauta para decidir cual palabra se adecua al contexto.