Ideally, the fluorescence intensity in the bound state is identical to that in the unbound state. However, it is not unusual for the fluorescence to change upon binding if there is some sort of interaction between the fluorophore and the binding partner. The fluorescence can increase or decrease, depending on the circumstances.

The problem with this phenomenon is that it distorts the value of the dissociation constant. For example, suppose the fluorescence decreases upon binding. The measured fluorescence intensities consists of low polarization light from the free fluorophore and high polarization light from the bound fluorophore. But the light from the bound fluorophore is under-represented because it is less intense than the light from the unbound fluorophore. This makes the binding look weaker than it actually is. It is possible to correct for this effect mathematically if the relative fluorescence intensities of bound and unbound fluorophores are known.

In your experiment, the rising anisotropy that occurred at high protein concentrations may be artifactual, due either to fluorescence of the added protein or light scattering (turbidity) from protein aggregates. You can measure this excess fluorescence by performing the same protein titration in the absence of the fluorophore (keeping all other aspects the same). You can even correct for the effect by subtracting the horizontal and vertical fluorescence intensities due to the protein alone from those of the protein+fluorophore at each protein concentration, prior to calculating the anisotropy.

I agree with Adam's points. But it would be much easier to comment on your results if you could provide more details such as what fluorophore are you using (I presume that one of your proteins is labeled with a probe) and what excitation and emission wavelengths are you using. In these case the experimental details can be critical to understand what is happening.