This paper develops a kernelized slow feature analysis (SFA) algorithm. SFA is an unsupervised learning method to extract features which encode latent variables from time series. Generative relationships are usually complex, and current algorithms are either not powerful enough or tend to over-fit. We make use of the kernel trick in combination with sparsification to provide a powerful function class for large data sets. Sparsity is achieved by a novel matching pursuit approach that can be applied to other tasks as well. For small but complex data sets, however, the kernel SFA approach leads to over-fitting and numerical instabilities. To enforce a stable solution, we introduce regularization to the SFA objective. Versatility and performance of our method are demonstrated on audio and video data sets.