One-dimensional models are presented for the macroscopic intracellular transport of vesicles and organelles by molecular motors on a network of aligned intracellular filaments. A motor-coated vesicle or organelle is described as a diffusing particle binding intermittently to filaments, when it is transported at the motor velocity. Two models are treated in detail: 1) a unidirectional model, where only one kind of motor is operative and all filaments have the same polarity; and 2) a bidirectional model, in which filaments of both polarities exist (for example, a randomly polarized actin network for myosin motors) and/or particles have plus-end and minus-end motors operating on unipolar filaments (kinesin and dynein on microtubules). The unidirectional model provides net particle transport in the absence of a concentration gradient. A symmetric bidirectional model, with equal mixtures of filament polarities or plus-end and minus-end motors of the same characteristics, provides rapid transport down a concentration gradient and enhanced dispersion of particles from a point source by motor-assisted diffusion. Both models are studied in detail as a function of the diffusion constant and motor velocity of bound particles, and their rates of binding to and detachment from filaments. These models can form the basis of more realistic models for particle transport in axons, melanophores, and the dendritic arms of melanocytes, in which networks of actin filaments and microtubules coexist and motors for both types of filament are implicated.