Using dielectric spectroscopy, we have studied different types of relaxation processes, namely, primary (alpha), secondary (beta), and other sub-T(g) processes, in the supercooled liquids of tritolylphosphate (TTP), 3-bromopentane (3BP), isopropylbenzene (IPB), glucose (GL), and also in the supercooled plastic crystals of cyclohexanol (CHOL) and camphor, over a wide frequency (10(-3)-10(6) Hz) and temperature (above 77 K) range. Asymmetric Cole-Cole plots are found at temperatures above T(g) in all the systems except camphor where they are very symmetric. TTP and 3BP are found to have weak sub-T(g) processes and the corresponding alpha process do not show significant change in the shape of Cole-Cole plots with temperature. TTP, 3BP, and IPB are found to possess at least two sub-T(g) processes (designated as beta and gamma processes, respectively) and the evidence for any of them to be intermolecular in nature is not strong. The origin of these processes probably lies in a side group and/or segmental rotation which still survive in the glassy state. In both GL and CHOL, the sub-T(g) process previously designated as the beta process by earlier workers is found to be non-Arrhenius in character representing another glass transition below the main T(g). Calorimetric evidence is provided for the purpose. The origin of this process is probably due to the "free" molecules. The origin of the various sub-T(g) processes has been discussed in greater detail.