A series of organic polymers and the military explosive cyclotrimethylenetrinitramine (RDX) were studied using the light emission from a femtosecond laser-induced plasma under an argon atmosphere. The relationship between the molecular structure and plasma emission was established by using the percentages of the atomic species (C, H, N, O) and bond types (C-C, C═C, C-N, and C≡N) in combination with the atomic/molecular emission intensities and decay rates. In contrast to previous studies of organic explosives in which C2 was primarily formed by recombination, for the organic materials in this study the percentage of C-C (and C═C) bonds was strongly correlated to the molecular C2 emission. Time-resolved emission spectra were collected to determine the lifetimes of the atomic and molecular species in the plasma. Observed differences in decay rates were attributed to the differences in both the molecular structure of the organic polymers or RDX and the chemical reactions that occur within the plasma. These differences could potentially be exploited to improve the discrimination of explosive residues on organic substrates with laser-induced breakdown spectroscopy.