Hi,
If you look at everything from the point of view of classical physics then everything is continuous. By continuous we mean that no matter how small you make the measurement time and where you look at it the signal level can always be resolved without loss of accuracy. So for example we might see a signal that is 2.4187348343384759128529688825232176523127653127653128129739122432328972342864342987 volts (and more digits after that) at a time t and also at a time t+1e-999999 seconds or at t+1e-5000 or at 1e+5000 seconds, even though we can not measure that in real life. So we can have a signal that has resolution 1e-6v, 1e-60v, 1e-600v, 1e-6000v, etc., with no limit to the resolution and no limit on what time it can occur given any starting time. Also, we can have the signal occur anywhere in space, at a distance of 1e-6 or 1e-8844 etc.
So then there are basically no limits on the freedom of the signal to appear any time, any place, or with any specific resolution, and amplitude and the place and time it appears next can be infinitesimally resolved in all cases.
In a discrete (in time) system the signals are taken to be ONLY at the sampling instants, and are taken to not even exist between these sample periods. So for example if we measure every second, then we can only say that the signal exists at t=0, t=1, t=2, t=3, etc., and we can not say that the signal exists at t=2.4 seconds for example.
I dont think there is anything in the universe that does this, including man made things, because there is nothing that does not exist for a short time and then suddenly exists again for an infinitesimally short time again and then disappears again, and not only that, but does this at a constant frequency. I seriously doubt there is anything like that in the universe even if we drop the constant frequency constraint, but of course we dont know everything about the universe just yet so maybe we'll find something in the future.
Quantization of light might be considered a discrete system, discrete in quantity though not in time. If we argue in favor of a time quanta, then maybe we can say that everything is discrete. There is one theory out there that takes everything to be quantized, including time and space. Maybe more discussion on this at some point.