Saliency models have been frequently used to predict eye movements made during image viewing without a specified task (free viewing). Use of a single image set to systematically compare free viewing to other tasks has never been performed. We investigated the effect of task differences on the ability of three models of saliency to predict the performance of humans viewing a novel database of 800 natural images. We introduced a novel task where 100 observers made explicit perceptual judgments about the most salient image region. Other groups of observers performed a free viewing task, saliency search task, or cued object search task. Behavior on the popular free viewing task was not best predicted by standard saliency models. Instead, the models most accurately predicted the explicit saliency selections and eye movements made while performing saliency judgments. Observers' fixations varied similarly across images for the saliency and free viewing tasks, suggesting that these two tasks are related. The variability of observers' eye movements was modulated by the task (lowest for the object search task and greatest for the free viewing and saliency search tasks) as well as the clutter content of the images. Eye movement variability in saliency search and free viewing might be also limited by inherent variation of what observers consider salient. Our results contribute to understanding the tasks and behavioral measures for which saliency models are best suited as predictors of human behavior, the relationship across various perceptual tasks, and the factors contributing to observer variability in fixational eye movements.