Hybrid systems of excitons strongly coupled to localized surface plasmons supported by metallic nanoparticles define a new approach to control light-matter interactions. Here, we report exciton-plasmon coupling in two-dimensional (2D) semiconductors, such as MoS2 and WS2, hybridized with silver nanoparticles. Prominent photoluminescence enhancement in monolayer MoS2 was observed with localized surface plasmon resonance (LSPR) tuned to the exciton resonance. By tuning the excitation energy, the contributions from near field enhancement and radiative emission rate enhancement via Purcell effect were resolved. Strong coherent dipole- dipole coupling between excitons and LSPR in resonant condition manifests as an electromagnetically induced transparency window in the extinction spectra of the localized surface plasmon. In this strong coupling regime a new quasi-particle, known as a plexciton, is expected to exhibit distinct properties, which exist in neither of the original particles. Our results demonstrate that 2D semiconductors hybridized with plasmonic structures not only hold great promise in the applications of energy- harvesting and light-emitting devices, but also provide an attractive platform for fundamental investigations of exciton-plasmon interactions in the strong coupling regime.