The most natural and numerous contributions of string theory to other fields are string theory's contributions to the most closely adjacent fields, mathematics and quantum field theory (both its conceptual understanding as well as model building).
Mathematics
String theory is the framework in which mirror symmetry was discovered; mathematicians have converted it into a subdiscipline of algebraic geometry that is studied by rigorous mathematical tools these days. Quite generally, much of algebraic geometry, especially topics related to Calabi-Yau manifolds, topology of higher-dimensional manifolds, K-theory, are using lots of tools that were first invented with the help of string theory – including topological string theory; the mechanisms of stringy tachyon condensation (K-theory), non-commutative geometry (which is naturally realized as string theory with a nonzero B-field) and others.
Quantum field theory: formal and conceptual part
In the context of the Western civilization, supersymmetry was born in the context of string theory – when Pierre Ramond was incorporating fermions into the old bosonic string theory. (Russians independently discovered supersymmetry purely by analyzing possible symmetries from a mathematical viewpoint.) String theory reasoning has also been important to discover many properties of the supersymmetric quantum field theories such as the $N=2$ gauge theories (Seiberg-Witten), and others.
Because of the AdS/CFT and other insights, people learned what physical phenomena dominate the strongly coupled limits of many quantum field theories.
Quantum gravity
These days, we consider the terms "quantum gravity" and "string theory" to be more or less synonyma because string theory is the only known, and quite likely the only mathematically possible, consistent quantum theory of gravity in dimensions 3+1 and higher. However, we may also view quantum gravity as a separate subject. If we do so, we may view string theory as a toolkit that has brought us many new important insights and answers to old questions. For example, the information is preserved when the black holes evaporate; topology of spacetime may change, and so on, and so on.
Quantum field theory: model building
Model builders propose possible new particles, forces, and phenomena that could be discovered by future particle physics experiments if they discover anything at all. The internal consistency and the consistency with the known facts about particle physics are the only constraints so there's a lot of room for model builders' imagination.
However, some of the most conceptually new and interesting possibilities were invented either because they were directly inspired by string-theoretical research, or the research of similar topics was continuing simultaneously in string theory and quantum field theory and the quantum field theory insights were found to be very naturally embedded in string theory – and string theory often provided physicists with new insights.
Various models of large extra dimensions and warped extra dimensions fall into both of these groups much like deconstruction and other quantum field theories with some new conceptual interpretations and behavior.
AdS/CMT and AdS/anything
The application of string theory tools to many other, unexpected disciplines exploded after the 1997 discovery of the AdS/CFT correspondence by Juan Maldacena. Conformal (scale-invariant) field theories are more or less omnipresent in physics and in very many of them, it's been proposed that the physics is equivalent to the physics of a quantum gravitational theory, string theory, in a particular curved Anti de Sitter (or similar) spacetime background with a dimensionality higher by one.
In this method, many physical objects that seemed to have nothing to do with fundamental physics were studied as manifestations of higher-dimensional AdS black holes. The examples include fluids – most famously, string theory naturally calculated the bound on the viscosity-entropy ratio (although "non-stringy" arguments for the same value were found later, too) – quark gluon plasma (comparisons with the RHIC collider), Fermi and non-Fermi liquids, superconductors, hydrodynamics etc. Various applications in this list are established to different extents.
The list of applications above is surely not exhaustive and I hope that other users will add complementary information.
