The rate at which genomes adapt to environmental changes and the prevalence of adaptive processes in molecular evolution are two controversial issues in current evolutionary genetics. Previous attempts to quantify the genome-wide rate of adaptation through amino-acid substitution have revealed a surprising diversity of patterns, with some species (e.g. Drosophila) experiencing a very high adaptive rate, while other (e.g. humans) are dominated by nearly-neutral processes. It has been suggested that this discrepancy reflects between-species differences in effective population size. Published studies, however, were mainly focused on model organisms, and relied on disparate data sets and methodologies, so that an overview of the prevalence of adaptive protein evolution in nature is currently lacking. Here we extend existing estimators of the amino-acid adaptive rate by explicitly modelling the effect of favourable mutations on non-synonymous polymorphism patterns, and we apply these methods to a newly-built, homogeneous data set of 44 non-model animal species pairs. Data analysis uncovers a major contribution of adaptive evolution to the amino-acid substitution process across all major metazoan phyla-with the notable exception of humans and primates. The proportion of adaptive amino-acid substitution is found to be positively correlated to species effective population size. This relationship, however, appears to be primarily driven by a decreased rate of nearly-neutral amino-acid substitution because of more efficient purifying selection in large populations. Our results reveal that adaptive processes dominate the evolution of proteins in most animal species, but do not corroborate the hypothesis that adaptive substitutions accumulate at a faster rate in large populations. Implications regarding the factors influencing the rate of adaptive evolution and positive selection detection in humans vs. other organisms are discussed.