Examples
A linear circuit is one that has no nonlinear electronic components in it. Examples of linear circuits are small-signal amplifiers, differentiators, and integrators, or any circuit composed exclusively of ideal resistors, capacitors, inductors, op-amps (in the "non-saturated" regime), and other "linear" circuit elements.
Some examples of nonlinear electronic components are: diodes, transistors when they are operated in saturation, and iron core inductors and transformers when the core is saturated. Some examples of circuits that operate in a nonlinear way are mixers, modulators, and digital logic circuits.
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