Whether common ancestors of eukaryotes and prokaryotes had introns is one of the oldest unanswered questions in molecular evolution. Recently completed genome sequences have been used for comprehensive analyses of exon-intron organization in orthologous genes of diverse organisms, leading to more refined work on intron evolution. Large sets of intron presence-absence data require rigorous theoretical frameworks in which different hypotheses can be compared and validated. We describe a probabilistic model for intron gains and losses along an evolutionary tree. The model parameters are estimated using maximum likelihood. We propose a method for estimating the number of introns lost or unobserved in all extant organisms in a study, and show how to calculate counts of intron gains and losses along the branches by using posterior probabilities. The methods are used to analyze the most comprehensive intron data set available presently, consisting of 7236 intron sites from eight eukaryotic organisms. The analysis shows a dynamic history with frequent intron losses and gains, and fairly — albeit not as greatly as previously postulated — intron-rich ancestral organisms.