Excitons, composite electron-hole quasiparticles, are known to play an important role in optoelectronic phenomena in many semiconducting materials. Recent experiments and theory indicate that the band-gap optics of the newly discovered monolayer transition-metal dichalcogenides (TMDs) is dominated by tightly bound valley excitons. The strong interaction of excitons with long-range electromagnetic fields in these two-dimensional systems can significantly affect their intrinsic properties. Here, we develop a semiclassical framework for intrinsic exciton polaritons in monolayer TMDs that treats their dispersion and radiative decay on the same footing and can incorporate effects of the dielectric environment. It is demonstrated how both inter- and intravalley long-range interactions influence the dispersion and decay of the polaritonic eigenstates. We also show that exciton polaritons can be efficiently excited via resonance energy transfer from quantum emitters such as quantum dots, which may be useful for various applications.