1. In a computing environment having a client computer, a system comprising: a main host system of the client computer; and a network event notification subsystem associated with the client computer, including a networking subsystem that communicates with a network server to act as a proxy for the client computer when the main host system of the client computer is in a sleep state, wherein the networking subsystem is configured to perform the following: receive a content or event notification from the network server; determine, according to a user-defined policy that indicates the relative importance of each of a plurality of different content and events, that the content or event is important enough to wake one or more selected individual components of the main host system to respond to the content or event notification; determine, according to a hardware wake policy that indicates a current battery level and current thermal level, that a minimum battery level threshold is currently met by the battery and that a maximal thermal level threshold is not being exceeded by the host system; based on the battery level and thermal level determinations and based on the indication of importance in the user-defined policy, determine the extent to which the main host system is to be awoken in order to process the content or event notification, wherein only the selected individual components of the main host system necessary to process the content or event notification are to be awoken, the system being configured to selectively wake any one or more of a plurality of different individual host system components; based on the determination, wake only the determined individual components of the main host system to respond to the content or event notification, such that those components of the main host system that are not needed to process the content or event notification are not awoken; and upon determining that the content or event notification has been processed, return the awoken components of the main host system to its sleep state.