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We consider passive inertial particles settling under the combined action of gravity and a Stokes drag in two-dimensional velocity fields with increasing complexity. The average settling speed is studied in simple steady and time-dependent cellular and in turbulent flows. Different regimes are identified in relation to the physical properties and complexity of the fields. While for steady and slowly varying weak cellular fields the settling velocity is a decreasing quadratic function of the Eulerian velocity, the same behaviour does not occur for actual turbulent fields. Large fluid velocities, on the other hand, generally speeds up the settling process. The relationships between settling times and the properties of particle trajectories in the different regimes are discussed.