That depends. I know, a "Clinton-esque" answer, but that's as close as you can accurately get.
Since we can neither create nor destroy matter (exception is nuclear fission, which brings up a whole new discussion), all things will eventually cease to be, at least in a form recognizable to us.
For example, since the body of some famous historical figure- such as Joan of Arc- has long turned to dust, and the organic matter has gone on to be recycled by plant, microscopic organisms, etc, the recycled matter that was at one time Joan of Arc, may be (in some small amount) scattered among many people walking around right now...
Consider, that the Oxygen molecules respirated by Jesus Christ, or Mohammed, or Adolf Hitler... Are still here. They may now be CO2, CO, or even be some of rusty metal on the car I'm restoring...
To say that all things cease to be, is putting too fine a point on it. That they cease to be recognizable, I would say is more likely... But, until we have the ability to completely obliterate particles of matter (ignoring the E=MC^2 issue), there is no possibility of all things "ceasing to be" from a material perspective...
FReegards,
The other problem with an infinite regression of time (or motion in the philosophical sense) is that an actual infinite series cannot exist by definition, since in becoming actual a series ceases to be infinite.
I've read that St. Thomas believed that the universe could be infinitely old, but only if it was co-extensive with its Creator. I'm ignorant of his argument, but I'll take his word for it.