Effective potentials have been used extensively as model molecular interactions to account for the thermodynamic properties of pure fluids and solutions. Here we develop the concept of effective potential and apply it to a variety of properties in the dilute- and dense-fluid states. We show how a simple kind of potential, named Approximate Non-Conformal (ANC), can be used effectively to calculate accurately a variety of thermodynamic properties of fluid substances. We present evidence for properties in the gaseous state (second and third virial coefficients), for the liquid-vapour coexistence and critical properties (T-c, V-c and P-c). Most gaseous-phase properties are obtained within estimated experimental errors. The molecular features whose effects have been incorporated into the ANC effective potentials are overlap, dispersion, electrostatic (dipolar and quadrupolar) and many-body interactions, and steric features such as elongation Applications to a selection of non-polar substances noble gas molecules, diatomics and light alkanes highlight the main features of the theory. New results include Gibbs ensemble Monte Carlo simulations of ANC fluids, an effective potential to account for many-body forces, prediction of critical temperatures and volumes, and we also prove a general relation satisfied by the critical temperatures of many substances. (c) 2007 Elsevier B.V. All rights reserved.