To what extent can speed of light be reduced? Light slows down upon entering different transparent objects, and the ratio is taken as refractive index of the object. If light can be slowed down, then is there a limit up to which it can be slowed down? If yes, then what is the minimum speed?
 A: The answers given here make me wonder, because I sense in here perhaps a misunderstanding. Or maybe I'm wrong, which might be more likely. :-)
The answers here refer to distances light travels. But as far as I understood, light is never slower than 299 792 458 m/s. I guess it may "look" like from a point of reference that light has slowed down, when a event happened, e.g. travelling on a warped Raumzeit. My belief is, that you have to take "Raumzeit" into account, which Einstein described in the Relativitätstheorie a couple of decades ago. Slowing down means losing energy. But "losing" energy is just a redshift in the frequency, but light is still on the same fast pace, as before.
So I would suppose, that light does not slow down. I don't say I'm right, but maybe this is a hint.
A: The short answer is that there is no known theoretical strictly positive lower bound to the speed of light. Any positive number, no matter how small, is possible, although limits are set for each candidate material, as I explain at the end of my answer.
One has to be pedantic to understand the lack of limitation to a more generalized "speed of light". From this pedantic standpoint, true light has only one possible speed, namely $c$. Now we need to understand that the electromagnetic disturbance that one sees in an optical material is not pure light but a quantum superposition of electromagnetic field states and excited "atom" states (where I use the word atom to mean any atom / molecule that interacts with the light). What this means is that the dispersion relationships and thus the group velocity for the disturbance changes from $c$ owing to the coupling between the light and atom states. A rough analogy is that the disturbance becomes slowed because light is absorbed by atoms, which linger in excited states a short time before re-emitting light, thus slowing the disturbance propagation down.
The more the superposition is dominated by the atom states, the slower the disturbance propagation will be. Slower pulses are achieved by (1) longer effective lifetime of each light-atom interaction, (2) higher interaction cross sections (3) density of interacting atoms. As the interaction cross section increases without bound, each emitted photon is almost certainly going to interact with the emitting atom's nearest neighbor. This means that the limiting speed for that particular material will be of the order of the atom lattice spacing divided by the interaction lifetime. An interaction lifetime of $1{\rm ns}$ with a $0.3{\rm nm}$ lattice spacing will give a propagation speed of the order of $30{\rm cm\, s^{-1}}$.
A: How the light slows down in a matter, it depends on the recipe of its refractive index. For common, ordinary materials it is in the range of 1-3.
Bose-Einstein condensates have an extreme refractional index, even millions or billions. In a BEC with a refractive index of $10^9$, the speed of light is only $30~\mathrm{cm/s}$.
Here is a relative old article from 1999 about the slowing of the light to around $50 ~\mathrm{km/s}$. There are recent results significantly improved even this.
The same scientist stopped the light later only two years and made it "restartable".
A: How would you define speed?
In case it has a direction:
The maximum slowdown you can get is 2C, this is achieved by using a mirror.
In case it is defined by the time taken to get from A to B
In case you would define speed by looking at the width of an object, where the light enters at point A, and leaves at point B, the following can be derived:

*

*The object may be a black box

*Inside the black box, there are 4 mirrors, the light initially moves north, then hits the first mirror at a 90 degree angle and is reflected east. Many kilometers to the east, the light hits another mirror at a 90 degree angle and is reflected north. After 1 meter, the light hits another mirror and is reflected west. Close to the first mirror it hits the fourth mirror, and is reflected north.

Now the resulting speed through the object can be made arbitrariliy slow (but positive) by moving the second and third mirror further back.
This example is somewhat contrived, but if I recall correctly, a laser actually uses a similar concept. (Keeping light 'in' for a while, and thus slowing it down by this definition.)
Otherwise
For other definitions, I would say the existing answers should suffice.
