Transition paths are brief excursions taken by molecules when they cross barriers separating stable molecular conformations. When observed in single-molecule experiments, they offer insights into the underlying reaction dynamics and mechanisms. A common model used to analyze transition paths assumes that the dynamics along the reaction coordinate is a memoryless, diffusive process. Recent work, however, suggests that memory effects are often important in the dynamics of the reaction coordinates that can be accessed experimentally. Here we study how memory affects the temporal duration of transition paths using the simple model of dynamics governed by a generalized Langevin equation with an exponential memory kernel. We discuss several approximate theories for the distribution and the mean of the transition path times and test them against numerical simulations. We find that the extreme case of long memory is particularly interesting in that it cannot be described by the existing approximations; yet it can be explained using the view where the non-Markov effects arise as a result of coupling of the reaction coordinate to an auxiliary degree of freedom.