Simple cooperative automatic retransmission request (ARQ) protocols are presented based on the selective amplified-and-forward (SAF) relaying method. Analysis shows that the temporal diversity of ARQs can be exploited with AF relaying only if the channel quality to the relay exceeds a threshold that depends on the source data rate requirement. Based on this analysis, an effective ARQ protocol is first developed from the concept of selective relaying to attain the full temporal diversity. Moreover, the notion of SAF relaying is further extended to systems with multiple relays to exploit the spatial and temporal diversities, incorporating the mechanism of opportunistic relaying. Two types of opportunistic-selective AF (OSAF) relaying methods are thus proposed for cooperative ARQs. Analysis shows that both OSAF protocols can offer much higher diversities than ARQ schemes with the typical AF relaying method. And the throughput of ARQs with OSAF is more robust to the variations of channel qualities and is close to their decode-and-forward counterparts.