Model-based clustering of motion trajectories can be posed as the problem of learning an underlying mixture density function whose components correspond to motion classes with different statistical properties. We propose a general framework for boosted modeling of mixtures of parametric densities. A density is represented as a parametric mixture of kernels where mixture components are now being added recursively, one at a time, until a best fit to data occurs and an optimal number of mixture components is selected. Optimal ML and MAP solutions to this problem are found using the functional gradient techniques. Unlike traditional mixture modeling techniques, the new method does not rely on random parameter initialization and exhaustive exploration of varying model orders (such as the number of mixture components.) The method justifies parameter estimation of new mixture components independently of that of the rest of the mixture, thus allowing tractable use of complex kernels such as HMMs or switching linear dynamic models. The relationship to traditional parametric EM-based mixture modeling algorithms is established. We demonstrate the utility of the new algorithm on the problem of discovering motion sequence clusters. Our generative modeling framework has an important advantage over nonparametric approaches in that it can be used for classification as well as synthesis of the learned motion categories.