Helium-like ions provide the most important x-ray spectral diagnostics in high temperature fusion and astrophysical plasmas. We previously presented computed collision strengths for O VII including relativistic fine structure, levels up to the n = 4 complex and radiation damping of autoionizing resonances. We have extended this work to other He-like ions (N, Ne, Mg, Al, Si, S, Ca). The calculations are carried out using the Breit-Pauli R-matrix (BPRM) method with a 31-level eigenfunction expansion. Collision strengths for the principal lines important in x-ray plasma diagnostics, w, x, y and z, corresponding to the four transitions to the ground level 1s^2 (^1S_0) \longleftarrow 1s2p \big(^1P^o_1\big), 1s2p \big(^3P^o_2\big), 1s2p \big(^3P^o_1\big), 1s2s (^3S_1) , are explicitly shown. We find the effect of radiation damping to be significant for the forbidden transitions in heavier He-like ions, which should affect the diagnostic line ratios. We extrapolated the collision strengths to their values at infinite energy using the Burgess-Tully extrapolation technique. This is required to calculate the Maxwellian average collision strengths at high temperature. We show that the coupling between dipole-allowed and inter-combination transitions affects increasingly the effective collision strengths for the n¹S₀-n'³P₁ transition as the charge of the ion increases. This clearly affects the treatment of the extrapolation towards the infinite energy point of the collision strength. This work is carried out as part of the Iron Project-RmaX network.