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We investigate transmission protocols for relay-assisted free-space optical (FSO) systems, when multiple parallel relays are employed and there is no direct link between the source and the destination. As alternatives to all-active FSO relaying, where all the available relays transmit concurrently, we propose schemes that select only a single relay to participate in the communication between the source and the destination in each transmission slot. The selection is based on the channel state information obtained either from all or from the last used FSO links. Thus, the need for synchronization of the relays' transmissions is avoided, while the slowly varying nature of the atmospheric channel is exploited. For the considered relay selection and all-active relaying schemes, novel closed-form expressions for the outage performance are derived, assuming the versatile Gamma-Gamma channel model. In addition, based on the derived analytical results, the problem of optimizing the optical power resources of the FSO links is addressed. Optimal and more computationally attractive suboptimal solutions are proposed that lead to a power efficient system design. Numerical results for equal and non-equal length FSO links illustrate the merits of the proposed relay selection protocols compared to the all-active scheme and demonstrate the significant power savings offered by the proposed power allocation schemes.