Does time exist in a vacuum? Imagine a perfect vacuum devoid of all matter and radiation. Irrespective of whether such a space can even exist, my intuition tells me that time would not exist within such a space. What this thought experiment tells me is that the human concept of time is basically that it's a measure of motion. Whether its a car speeding down a highway, skin on your face as the years go by, or photons, it's really all about motion. Now what about something like a gravitational field? Could that also be excluded from acting within a perfect vacuum?
 A: Assuming you're willing to accept General Relativity as a valid theory, your question has a well defined answer because we can solve the equations of GR for an empty universe. The result (well, the simplest result) is Minkowski spacetime.
You might think that nothing much can happen in an empty universe, but even though no matter or energy is present there can still be gravity waves. Indeed it's just possible, though sadly the evidence is against it, that you could have stable structures called geons that are built only from gravitational radiation.
Anyhow the point is that even a completely empty universe can have a dynamical structure and hence time evolution. So time does still exist even in a completely empty universe.
A: 
Now what about something like a gravitational field? Could that also be excluded from acting within a perfect vacuum?

As pointed out in this Wikipedia article on gravitational shielding, the ability to shield gravitational fields would violate the equivalence principle which is inconsistent with both Newtonian mechanics and Einstein's general relativity.  I.E. the ability to shield gravity is inconsistent with everything we know about gravity.  Practically, this is also related to the fact that mass comes with only one sign.
A: Isn't saying that time doesn't exist without motion equivalent to saying that sound doesn't exist when no one is around to hear it? You can't rule out time's existence in this way. Then again, why focus on time? When you propose an empty space, does space exist? Normally space is detected as a separation between objects. If no objects exists, as per scenario envisioned, would space exist when no one is around to measure or view it? In both cases I would argue that space and time exist regardless of the presence of particles and their motion, and indeed, regardless of the presence of an observer.
A: I think that using the concept of vacuum makes it harder to explain your question, because with the absence of matter you are moving towards the absence of Universe. I learned from the other answers that there is still energy and waves in vacuum, this is why I say "moving towards the absence of Universe", which I think it's not what you wanted to aim.
I myself asked this question long ago but I prefer to think in absolute zero, in which you are moving towards the absence of motion, like you describe. From Wikipedia I just learned that in absolute zero there is still a minimum energy state, but the reason I prefer using absolute zero instead of vacuum is because you still have matter in it, and can concentrate only in the (non)existence of Time.
So, ending with all motion would probably require ending with the Universe, which is not what we want to do here. Thus, I prefer to pose the question in the following way: is Time different from Space or a redundant dimension?
I think Time is redundant. You can refer to any point in Time (abstract concept) by describing the configuration of Space (all particles of the Universe). Using that configuration of Space and the laws of Physics you can predict the next configuration of Space. So, using the abstract concept of Time is just a way of referring to a configuration of the Universe in a practical way.
I hope I have improved my answer by slightly modifying your question, since I've also been through that line of thought. To better answer your question there is this book "The End of Time" by Julian Barbour. It was very reassuring to know there were more people to think about Time the way I do. Maybe you feel the same.
A: You people make this overly complicated. If the vacuum exists, time absolutely exists as well.
For example, if the vacuum were to exist near a source of radiation, particles. They could enter the given vacuum as time passes by so time absolutely exists. 
also, time as a count of existence progressing, also must be identically throughout the universe to our existence in and of itself, whereby a time period passed on earth is the sane time period passed in a vacuum on the other side of our universe.  
