ABSTRACT We compile a catalogue of low-mass and high-mass X-ray binaries, some recently reported binaries that likely host a neutron star (NS) or a black hole (BH), and binary pulsars (a pulsar and a non-degenerated companion) that have measured systemic radial velocities (γ). Using Gaia and radio proper motions together with γ, we integrate their Galactic orbits and infer their post-supernova (post-SN) 3D peculiar velocities ($v_\mathrm{pec }^{z=0}$ at Galactic plane crossing); these velocities bear imprints of the natal kicks that compact objects received at birth. With the sample totalling 85 objects, we model the overall distribution of $v_\mathrm{pec }^{z=0}$ and find a two-component Maxwellian distribution with a low- ($σ _v ≈ 21\, \mathrm{km s^{-1}}$) and a high-velocity ($σ _v ≈ 107\, \mathrm{km s^{-1}}$) component. A further comparison between distributions of binary subgroups suggests that binaries hosting high-mass donors/luminous companions mostly have $v_\mathrm{pec }^{z=0}\lesssim 100\, \mathrm{km s^{-1}}$, while binaries with low-mass companions exhibit a broader distribution that extends up to $∼ 400\, \mathrm{km s^{-1}}$. We also find significant anticorrelations of $v_\mathrm{pec }^{z=0}$ with binary total mass (Mtot) and orbital period (Porb), at over 99 per cent confidence. Specifically, our fit suggests $v_\mathrm{pec }^{z=0}∝ M_\mathrm{tot}^{-0.5}$ and $v_\mathrm{pec }^{z=0}∝ P_\mathrm{orb}^{-0.2}$. Discussions are presented on possible interpretation of the correlations in the context of kinematics and possible biases. The sample should enable a range of follow-up studies on compact object binary kinematics and evolution.