Does time exist?

I was reading Stephen Hawking's book, " A Brief History of Time", the other day, and it got me thinking. While the book( at least till the part i've reached) deals more with the existence of the universe and the various theories for its existence and formation, and whether time before the creation is relevant or whether it can be said that since it is totally different from the time after the formation of the universe, it can be neglected as it has no bearing whatsoever.
My question if somewhat more fundamental and yet more tricky to answer as as definite one. The thought that popped into my head was, What exactly is time?, and Does time even exist? Most of us keep talking about how much time we spend doing something, or how little time there is to do things, but how many of us have actually even given a thought as to what time actually is? Have you ever even thought of time as a quantity beyond that which we check on our watches? When we say, where has the time gone? or How the time flies? What do we mean, for all we know time may not even exist, so the question of it going or flying somewhere doesnt even arise.
This really got me intrigued and i decided to ask a couple of my friends. When i asked them if time existed, they all replied in the affirmative. When asked to define time, they all came up blank. Cant exactly fault them for that either, after all geniuses and scholars for years have struggled to come up with a definition of time.
Finally, frustrated, i decided to check out that all knowing source of information online, Wikipedia. Turns out, as far as the very concept of time is concerned, no one is really sure. They've mentioned the various theories, linear time, circular time, etc., all such complicated stuff, but unfortunately, for me atleast, it still doesnt answer my question as to What time is and does it exist.
Everyday we hear people speak about the importance of time, Time is money etc, watches and clocks invented to measure time with a high degree ofprecision. But, all this without being sure of what time actually is. It just goes to show how much the very concept and meaning of time has been obscured by the way it has been used.
It is somewhat surprising if you realize that our entire world revolves around this concept known as "TIME", whose definition we do not know, or for that matter, even its existence. What will happen to all our atomic clocks, watches, and very principles, if one fine day, some scientist comes along and proves that "Time" , in fact, does not exist?
So, at the end of this rather lengthy and confusing post, i still havent answered my first question. Will it ever be answered, only time will tell.
Oops! Cant even say that, coz I dont know what time is or if it even exists, do I?