We present maximum-likelihood search methods for time-dependent fluxes from point sources, such as flares or periodic emissions. We describe a method for the case when the time dependence of the flux can be assumed a priori from other observations, and we additionally describe a method to search for bursts with an unknown time dependence. In the context of high energy neutrino astronomy, we simulate one year of data from a cubic kilometer scale neutrino detector and characterize these methods and equivalent binned methods with respect to the duration of neutrino emission. Compared to standard time-integrated searches, we find that up to an order of magnitude fewer events are needed to discover bursts with short durations, even when the burst time and duration are not known a priori.