Well that is quite a good question. The only facts I can back up that time may have some form of existence is this:
24 hours in a day.... 24 beers in a case.. Coincidence? I think not.
Keep in mind as "time" passes by to not take it for granted. Also, don't piss off your kids. When your "time" is near, they choose your nursing home. x.x
"Does killing time damage eternity?"
Back on topic now.
Time is merely a measurement tool. Just as we made up charts and tables to keep track of things like height, weight, length, there is time. So it's existence is simply based on how you look at it. If you look at it as a tool that we developed over time, yes. It does exist. If you look are looking at it as some mythical thing passed on from the start of Earth, then it is nothing more than a unicorn.
Keep in mind at one point in time, there was no measurement of time. There was just an estimate on how long you felt it would be until the sun goes down.
That's my thoughts on it.