Are there applications of supersymmetry in other branches of physics other than high energy/particle physics?
In 1980, Hermann Nicolai proved that the existence of a supersymmetry is equivalent to the statement that there exists a change of variables to turn the time evolution in the path integral into a stochastic equation. This change of variables is explicity known only for a handful of relativistic models, but it is known explicitly for all stochastic equations, because they are already stochastic equations--- there is nothing to transform.
Stochastic equations are the domain of condensed matter physics, and supersymmetry in these systems was discovered by Parisi and Sourlas in the early 1970's, almost simultaneously with the high energy discoveries. The stochastic applications are enormous, including SUSY QM, supersymmetric disorder averaging, supersymmetric phase transitions, etc. The applications are arguably more varied and interesting than those in high energy, because there is no necessary requirement of quantum unitarity, and you're allowed to play in swampland.
In nuclear physics, there is also an experimentally confirmed approximate supersymmetry between large nuclei with total spin differing by half.
Besides supersymmetric quantum mechanics and supersymmetric integrable systems, there is, e.g., supersymmetric fluid dynamics. Of course, nowadays, it seems that almost any kind of system may be derived as some limit of String Theory, so whether it is outside or inside of high energy/particle physics is a matter of definition.
There are interesting applications in nuclear physics: http://arxiv.org/abs/nucl-th/0402058