I believe time is the measurement of a universal speed at which matter exists. If my atoms move at the same rate yours do (and everyone else on the planet), we all see time at the same speed. This might be different for other types of matter, or in other parts of the universe. Certainly it would be different around strong gravitational fields.
As far as the circle idea, I find it very unlikely that time itself, being only a measurement, should take on a property like that. But, since matter is tied to time-- in that matter travels over a distance in a period of time, you could be asking if the universe will collapse on itself. Of course that is a common theory, but I still don't buy it.