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Two example are certainly the electromagnetic field and the gravitational field.

The Higgs field, weak fields, and strong fields are too short ranged to operate on macroscopic scales. Moreover, the excitations of spinor fields cannot occupy the same state and therefore no macroscopic field excitations can exist.

Are there any other examples of macroscopic, classical fields?

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    $\begingroup$ Water waves, sound waves, …. $\endgroup$ – jim Sep 16 at 11:16
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    $\begingroup$ The Higgs has a nonzero expectation value, so you could argue that a constant-valued higgs field absolutely does exist classically. $\endgroup$ – Jerry Schirmer Sep 16 at 13:57
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Any quantity that varies in space and time can be described as a field. For classical fields this includes quantities like temperature, pressure, density, etc., which are all scalar fields, and streamlines of fluid flow, such as wind in the air, or currents in water, etc. that are vector fields.

As mentioned in a comment, perturbations in these fields produce pressure waves or sound, surface water waves, etc.

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