Yes, light can be brought to a complete halt under the right conditions.
To understand how this happens you need to understand what is going on when light slows down in a medium. Light is an oscillating electromagnetic field, and when it passes though anything that contains charged particles (i.e. any matter made from electrons and protons) the electric fied of the light interacts with those charges.
When the light interacts with the charges we have to describe the light/matter system by a new wavefunction that includes all the interacting components. This means the light is not longer purely light - we have a quantum system that mixes up the light with the charged particles. If this mixing is very strong it produces a quasiparticle called a polariton. The polariton is a massive particle so it moves at less than the speed of light.
Under normal circumstances, e.g. light passing through glass, the interaction of the light and the medium is relatively weak and we probably wouldn't use a polariton description. Instead we'd use a classical description as described very nicely in the answers to Why do prisms work (why is refraction frequency dependent)?.
However it is possible to make systems that interact very, very strongly with the light. Specifically Bose-Einstein condensates. This interaction can be so strong that the polaritons become essentially motionless i.e. the light is brought to a stop. This was first achieved in 2001 by a group at the Harvard-Smithsonian Center for Astrophysics, who managed to bring light to a stop in a gas of rubidium atoms. At about the same time a group in Harvard achieved the same result using a Bose-Einstein condensate made from sodium atoms.
The experiments mentioned above require rather extreme conditions to work, but they involve basically the same physics that causes light to slow down by a factor of about 1.5 in glass.
