At the cost of predicting a whole set of new particles, SUSY provides a fix for a number of the standard model’s problems. For example, the standard model predicts a divergent value for corrections to the Higgs boson’s mass, but SUSY offers a way around this problem, provided the sparticles aren’t too heavy . Another exciting possibility is that SUSY provides a way to unify the different forces coupling constants at very high energy. There is no a priori requirement that this must happen, but the potential unification of the electroweak and strong forces has an elegance that is tantalizing . Many versions of SUSY have an extra conservation law that would prohibit the decay of the lightest SUSY particle. Not only would this particle become a dark matter candidate, but in this context SUSY can be used to provide both a full calculation of early universe physics and the dark matter relic density, a central problem in modern cosmology . Finally, SUSY allows a possible connection to quantum gravity through superstring theory.
All that, and it might even clean your windows!
Still, we do live in a very exciting time, and the LHC will discover (if not already) new physics even if we don't find the Higgs or any SUSY's sparticles. Considering that no new particle colliders are in the books to being built, we will have to live with the LHC for quite a number of years from now.