It's possible to make an estimate of the amount of baryons in the observable universe. But it's more difficult to make an estimate of anything else. It gets particularly more difficult when you consider things like photons, because they can pop in and out of existance, i.e. the number of photons is not constant. Actually, that is true for all elementary particles, since they are considered as excitations of quantum fields in most modern physics theories. Thus, the number of particles is not constant. But the heavier the particle, the less likely it will pop in existance. And if it's too heavy, it'll decay in lighter, more stable particles. So maybe you'll have something a couple of orders bigger than the amount of baryons, but probably not much larger.
Then, there is dark matter, of which we don't really know much. So, I have no idea if an estimate has been attempted of the amount of dark matter particles. Any estimate will be highly dependent on the theory we have for these particles.
In his book The Emperor's New Mind, Penrose estimates the number of baryons in the observable universe to be of the order of $10^{80}$. This seems to confirm it.