Of course-excitations in a fluid are a typical example. Cf. any textbook on hydrodynamics. 

There are two uses of the word. One refers primarily to fermions (electrons dressed by excitations), and I presume this is what you are referring to. In most of these instances, the fact that the electron gas is degenerate, and so that the Fermi exclusion principle is important, makes extension to classical statistical mechanics impossible.

On the other hands, such quasiparticles as phonons, which are bosons, give rise to classical fields, such as the elastic field. Whether these might deserve the name of quasiparticles, is an issue of language. I would probably prefer another name.

Thanks everyone for your answers. By quasiparticles what I had in mind is classical particles dressed with their classical correlations such that the dressed classical particles can we treated with weak coupling mean field theory in the Landau sense. Or in the other words, the intermediate/strong coupling classical system is mapped to a weak coupling system. Also it must satisfy the fluctuation dissipation theorem , response chi = S(k), static structure factor. Is there any literature on that? Thanks in advance.

Such a particle can be considered the one appearing in the two-body central force problem, the one with mass μ=(m1m2)/(m1+m2), when the two-particle system converts into a one-dimensional problem.

The normal modes in the classical theory of small oscillation typify quasiparticles.