The translational diffusion constant, D, of dioxygen, O-2, has been measured in the odd n-alkanes n-C7H16 to n-C15H32, two branched alkanes (isooctane and squalane), and several cycloalkanes (cyclohexane, methylcyclohexane, n-butylcyclohexane, dicyclohexyl, cis-decalin, and trans-decalin). The D values were determined using Taylor-Aris dispersion theory in solutions drawn through a microcapillary by reduced pressure. The initial analysis of the data was in terms of the Stokes-Einstein relation (D = k(B)T/6 pi eta r). In both the n-alkanes and cycloalkanes, the values of the hydrodynamic radius r for O-2 are smaller than its known dimensions and decrease as the viscosity r increases, i.e., O-2 is diffusing faster than predicted by a constant solute "size." The data can be fitted to D/T = A/eta(p) with p < 1 (p = 1 for the Stokes-Einstein relation). When the data for the odd n-alkanes are combined with our earlier results for O-2 in the even n-alkanes (n-C6H14 to n-C16H34, Kowert, B. A.; Dang, N. C. J. Phys. Chem. 1999, 103, 779), we find p = 0.553 +/- 0.009. For O-2 in the cycloalkanes the fit gives p = 0.632 +/- 0.017. The data for isooctane and squalane are in approximate agreement with the n-alkane fit. The D values are also discussed in terms of computer simulations for small penetrants in hydrocarbons, the molar volumes of the solvents, and free volume approaches. A correlation between the p values and results of the free volume analyses is noted and discussed.