As jheindel has previously pointed the interaction has no limit. What you are probably looking for is the distance at which the interaction energy becomes smaller than thermal energy at a given temperature. When the interaction is smaller then thermal motions govern what happens not the intermolecular interaction. Thermal energy at $300$ K is $k_BT = 1.38\cdot10^{-23}\cdot 300 = 4.1\cdot 10^{-19}$ J.
The interactions all have the general form $E=V/(\epsilon r^n)$ where $V$ is scaling term: for example for charge - charge interaction $n=1$ and $V=q_1q_2e^2/(4\pi\epsilon_0)$ where $q$ are the charge signs, $e$ the charge on the electron and $\epsilon _0$ the permittivity of free space $8.854\cdot10^{-12}$. Finally $\epsilon$ is the solvent dielectric constant, cyclohexane = 2, water = 78.
The interaction energy between two charges, say sodium and chlorine ions, in vacuum separated by 0.3 nm is approximately $190k_BT$, but in water this only $2.4k_BT$ so the distance at which the intermolecular interaction is important depends very much on the conditions. The reason that $\epsilon$ has such an effect is that the high dielectric solvent attenuates the electric field around an ion or dipole.
There are other types of interaction ion-dipole, dipole-dipole, induced dipole-induced dipole and so on that have energies that depend, where appropriate, on the magnitude of the dipole, polarisability, the relative dipole orientation and various powers of separation $1/r^n$. For example for dipole-dipole interaction with fixed dipole directions the relative dipole angle is important and $n=3$ but for freely rotating dipoles the dipole angle is averaged out resulting in $n=6$ (Keesom energy). London dispersion force (induced dipole-induced dipole) depends on each molecule's polarisability and has $n=6$,in comparison charge-dipole interaction has $n=4$.
If you look these up to calculate particular interactions note that many authors quote values in vacuum and so ignore the solvent dielectric constant. You can include this by changing $\epsilon_0\to \epsilon_0\epsilon$.