We propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients. The method is applicable when the individual curves are sampled at variable and irregularly spaced points. This produces a low rank, low frequency approximation to the covariance structure, which can be estimated naturally by the EM algorithm. Smooth curves for individual trajectories are constructed as BLUP estimates, combining data from that individual and the entire collection. This framework leads naturally to methods for examining the effects of covariates on the shapes of the curves. We use model selection techniques---AIC, BIC, and cross-validation---to select the number of breakpoints for the spline approximation. We believe that the methodology we propose provides a simple, flexible, and computationally efficient means of functional data analysis. We illustrate it with two sets of data.