In this paper, we present a diversity gain analysis for free-space optical (FSO) diversity systems operating in log-normal atmospheric turbulence channels. We consider a multi-input multi-output (MIMO) system and two decode-and-forward (DF) relay-assisted systems based on either serial (i.e., multi-hop transmission) or parallel (i.e., cooperative diversity) configurations. We adopt the recently introduced so-called "asymptotical relative diversity order" (ARDO) in our analysis and derive ARDOs for FSO diversity systems under consideration. Assuming M transmit and N receive apertures in MIMO scheme, we demonstrate that an ARDO of 4 sigma(2)(x)/ln(1+(exp(4 sigma(2)(x))-1)/MN) is achievable where sigma(2)(x) is the variance of the fading log-amplitude. For weak turbulence conditions (i.e., sigma(x) similar to 0.1), ARDO is well approximated as MN. For DF relaying schemes with K relays each of which is equipped with single transmit/receive apertures, we demonstrate that ARDOs of (K+1)(11/6) and 2(11/6) K are achievable, respectively, for serial and parallel relaying configurations.