Quantum chromodynamics (QCD) provides the most well-known example: see the article on QCD vacuum for details. Experimentally it is seen that the masses of the octet of pseudoscalar mesons (such as the pion) are very much lighter than the next heaviest states, ie, the octet of vector mesons (such as the rho).
In QCD this is interpreted as the spontaneous symmetry breaking of a version of QCD with 3 flavours of massless quarks. Such a theory has global chiral flavour symmetry. Through SSB this is broken to the diagonal , generating eight Goldstone bosons, which are the pseudoscalar mesons which lie in the octet representation of flavour .
In real QCD, the quark masses break the chiral symmetry explicitly. The masses of the true pseudoscalar meson octet are found by an expansion in the quark masses which goes by the name of chiral perturbation theory. The internal consistency of this argument is further checked by lattice QCD computations allow one to vary the quark mass and check that the variation of the pseudoscalar masses with the quark mass is as required by chiral perturbation theory.