Quantum simulators are a promising technology on the spectrum of quantum devices from specialized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behavior to explore and solve hard scientific, engineering, and computational problems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special purpose simulators to flexible programmable devices. These developments have enabled a convergence of ideas drawn from fundamental physics, computer science, and device engineering. They have strong potential to address problems of societal importance, ranging from understanding vital chemical processes, to enabling the design of new materials with enhanced performance, to solving complex computational problems. It is the position of the community, as represented by participants of the National Science Foundation workshop on \textquoteleft\textquoteleftProgrammable Quantum Simulators,\textquoteright\textquoteright that investment in a national quantum simulator program is a high priority in order to accelerate the progress in this field and to result in the first practical applications of quantum machines. Such a program should address two areas of emphasis: (1) support for creating quantum simulator prototypes usable by the broader scientific community, complementary to the present universal quantum computer effort in industry; and (2) support for fundamental research carried out by a blend of multi-investigator, multidisciplinary collaborations with resources for quantum simulator software, hardware, and education. This document is a summary from a U.S. National Science Foundation supported workshop held on 16-17 September 2019 in Alexandria, VA. Attendees were charged to identify the scientific and community needs, opportunities, and significant challenges for quantum simulators over the next 2-5 years.