In this work, the heat transfer and fluid flow analyses are employed to optimize the geometry of the pin-fin heat sinks. An entropy generation minimization method is employed to optimize the overall thermal performance and behavior of pin-fin heat sinks. The performance of the heat sinks is determined by its thermal resistance and pressure drop, since they significantly influence the thermal resistance during forced convection cooling. The optimum design of heat sink for in-line and staggered alignments with circular, square, rhombus, rectangular, and elliptical configurations are investigated, and the thermal behavior is compared. The entropy generation rate is developed using mass, energy, and entropy balance over the control volume. The formulation for the dimensionless entropy generation rate due to heat transfer and due to fluid flow (pressure drop) is obtained in terms of fin geometry, thermal conductivity, pin-fin alignment, Reynolds, and Prandtl numbers. Using an energy balance equation over the same control volume, the average heat transfer coefficient for heat sink is developed, which is a function of the heat sink material, fluid properties, fin geometry, pin-fin alignment. The selected materials are plastic, aluminum, and copper. Thermal and hydrodynamic analysis of pin-fin heat sink are performed using parametric variations of each design variable, including pin diameter or side, pin height, approach velocity, number of pin-fins, and thermal conductivity of the material. Optimization of heat sink designs and parametric behavior are presented and compared based on the selected pin-fin configurations, alignment, and material property. The results indicate that geometries of circular and elliptical shapes provide more favorable conditions for heat transfer than that of square, rectangular, and rhombus shapes. In all cases, optimum size of staggered alignment is better than in-line alignment. In a particular pin-fin configuration, entropy generation rate is comparatively elliptical circular rhombus rectangular square pin-fins. The optimum entropy generation rate moves down as the thermal conductivity of the fin material increases. Copper fin gives the best performance, and if the weight of the heat sink is a constraint, the aluminum fin would be preferable. However, the optimum diameter for the selected materials is almost the same. The optimum entropy generation rate moves down again with the thermal conductivity of the fin material, which shows the best performance of copper fins for the same approach velocity. Also, the optimum approach velocity for the selected materials is almost the same. The entropy generation rate decreases with the increase in thermal conductivity for the same number of fins and under the same operating conditions. Also, the optimum fin length increases with thermal conductivity of fin materials. The results enable the designer to quickly and easily access the merits of pin-fin geometries for specific design conditions and for selecting the optimal dimensions of fin and material.