Could a photon travel faster than the speed of light in vacuum? If the cosmic speed limit is the speed of light in vacuum, then what happens when a photon traveling through space meets gravity? Wouldn't gravity pull on the photon that's already traveling at max speed, thus making it ever-so-slightly faster?
 A: No, the photon would still go at c. E = hf for a photon. E is energy, h is a special number called Planck's constant, and f is frequency (also sometimes people use v instead of f). Instead of speeding up the photon, the gravity would increase the frequency of the light. For example, a red beam of light, pulled by gravity, might have its frequency increased so that it becomes blue.
A: In all references frames, due to special relativity, the velocity of a photon is always the speed of light, denoted $c$. If we consider a photon in spacetime, with a metric $g_{\mu\nu}$, the situation does not change; it must travel at the speed of light. However, virtual photons are off-shell, meaning they do not satisfy,
$$E^2 = p^2c^2$$
i.e. the relativistic dispersion relation (with $m=0$), and hence may travel faster than the speed of light.
A: Photons travelling inbetween two parallel conducting plates (travelling in the direction parallel to the plates) will travel slightly faster than the speed of light in an ordinary vacuum (the vacuum between the plates is known as a "Casimir vacuum" which has different properties from an ordinary vacuum). This effect is known as the Scharnhorst effect. While the photons do travel faster than light, this cannot be exploited to produce a violation of causality as is shown here.
A: Any photon that's moving away from the milky way is travelling faster than c relative to us because the space in between is expanding. There are even galaxies that move away from us faster than c but they are beyond the horizon of the visible universe.
