Charles Babbage's vision of computing has largely been realized. We are on the verge of realizing Vannevar Bush's Memex. But, we are some distance from passing the Turing Test. These three visions and their associated problems have provided long-range research goals for many of us. For example, the scalability problem has motivated me for several decades. This talk defines a set of fundamental research problems that broaden the Babbage, Bush, and Turing visions. They extend Babbage's computational goal to include highly-secure, highly-available, self-programming, self-managing, and self-replicating systems. They extend Bush's Memex vision to include a system that automatically organizes, indexes, digests, evaluates, and summarizes information (as well as a human might). Another group of problems extends Turing's vision of intelligent machines to include prosthetic vision, speech, hearing, and other senses. Each problem is simply stated and each is orthogonal from the others, though they share some common core technologies.