Is there any speed difference between blue or red light? Is there ever a speed difference? Or do all types of light move at the same speed?
The speed of light in vacuum is constant and does not depend on characteristics of the wave (e.g. its frequency, polarization, etc). In other words, in vacuum blue and red colored light travel at the same speed c.
The propagation of light in a medium involves complex interactions between the wave and the material through which it travels. This makes the speed of light through the medium dependent on multiple factors which include the frequency (other example factors being refraction index of the material, polarization of the wave, its intensity and direction).
The phenomenon due to which the speed of a wave depends on its frequency is known as dispersion and is the reason why prism and water droplets separate white light into a rainbow.
Since no one else has mentioned it ...
If you want to have a better conceptual understanding of the apparent slowing of light (and other electromagnetic waves) in materials, I strongly suggest reading Richard Feynman's lectures, especially Chapter 31 of volume I. That will give you much more explanation than is possible in this forum.
Recall that light can travel through a medium, like air or water or glass. You can measure the speed of light in any of these media. You can also pass light through a vacuum where there is just empty space. Think of the light coming from the sun. In empty space, all colors travel at the same speed called c. Light of different wavelengths, or colours, travels at different speeds when they travel through any medium other than vacuum. That last statement is not exactly true but the reasons are complicated and you can just look up solitons. Red light travels faster than blue in glass.
As far as we know, light is mediated by a particle without rest mass. Special relativity says that such a massless particle's speed must always be observed to be $c$, irrespective of the observer's motion. In general relativity, a massless particle's speed as measured locally is also always $c$. No experiment so far has detected a measurable difference between the speed of light of any color and $c$. So experimentation tells us that light of all "kinds" and colors moves at $c$ and relativity gives us insight into how this comes about.
When it interacts with matter, the speed of the disturbance arising from excitation by light can have different speeds. We now have a quantum superposition of light and excited matter states, so, although many people would call me pedantic, this isn't really light proper. Classically you can think of this as like a game of "Whisper Down the Lane": an atom of the medium absorbs light, dwells in an excited state, then re-emits a new photon. The net result is a slowed propagation, but the "light" part of the disturbance still travels at $c$. Depending on the kind of medium involved, there can be all kinds of dependence of propagation speed on color: as in Bill N's answer, Feynman gives a most excellent classical description. My attempt at a quantum explanation is here.