Recently, the study of I/O-efficient algorithms has moved beyond fundamental problems of sorting and permuting and into wider areas such as computational geometry and graph algorithms. With this expansion has come a need for new algorithmic techniques and data structures. In this paper, we present I/O-efficient analogues of well-known data structures that we show to be useful for obtaining simpler and improved algorithms for several graph problems. Our results include improved algorithms for minimum spanning trees, breadth-first search, and single-source shortest paths. The descriptions of these algorithms are greatly simplified by their use of well-defined I/O-efficient data structures with good amortized performance bounds. We expect that I/O-efficient data structures such as these will be a useful tool for the design of I/O-efficient algorithms.