Not in any reasonably modern system. The state in this case is the exact sequence of bits contained in RAM and on your hard drive, which might as well be infinite (lets ignore for a moment that your computer is connected to the Internet and to real entropy sources, which really do make things infinite).
Some napkin math: if you've got a terabyte hard drive and 32 gigs of RAM, then there are approximately 2^(1,032 * 1024 * 1024) states your computer might be in, which is about 1.79 * 10 ^ 325,753,719. It can be hard to conceptualize numbers at that scale, but a fun illustration is that it is so big that the number itself would not fit on many laptops. It is infinite for any useful sense.
For comparison, there are an estimated 10^86 atoms in the observable universe -- if each atom in the universe was in fact its own universe, and each atom in all of those universes was its own universe, and so on... you'd have to go four layers deep to start talking comparable numbers here.