Discusses the growing customer base for remote-access computing, examines the motivations for this growth, and extends these motivations to a larger scale to demonstrate the need for networks of computers. Current evolution and experimentation in resource sharing via networks of computers involves the interconnection of heterogeneous computing resources. The Defense Advanced Research Projects Agency's Network (ARPANET) is dicussed as an example. It is predicted that networks of computers will continue to grow as supplements to conventional time-sharing and will double the current time-sharing systems' capacities by 1977. This trend may lead to a computer utility where computer resources will be available and marketed the same as electric power and telephone services. While it appears that neither technology nor economics is a significant impediment to the growth of networking--the ARPANET and others show the technical feasibility and economic desirability of networks of computers--political, legal, and social problems may pose even greater obstacles. 21 pp. Ref.