The peroxide effect (anti-Markovnikov addition to alkenes) is observed with

For HCl the propagation step in which the carbon radical abstracts H from the strong H-Cl bond is endothermic, and for HI the addition of $\mathrm{I}\cdot$ to the double bond is unfavourable. Only HBr has both propagation steps favourable, so the peroxide effect is seen only with HBr.