The first application (of which I'm aware) of the Killing superalgebra was to perform a general (if shallow) check of the AdS/CFT correspondence by matching the symmetries across the correspondence; that is, showing that the Killing superalgebra of AdS backgrounds on the supergravity side agrees with the expected superconformal algebra of the dual field theory. Such a general check was made possible because in order to compute the Killing superalgebra of the AdS backgrounds it was not necessary to know the explicit form of the Killing spinors. By employing Bär's cone construction, it is possible to reduce the computation of the Killing superalgebra to representation theory alone.
A more structural application of the Killing superalgebra is in the context of the homogeneity conjecture. It is an empirical fact that all known supergravity backgrounds preserving a fraction ν > ½ of the supersymmetry are (locally) homogeneous; that is, the Lie group of automorphisms of the background acts locally transitive on the spacetime. The homogeneity conjecture states that this is true. In 2004, Patrick Meessen contacted me with some questions about this conjecture and a possible line of attack. At the end of the day, though, Patrick, Simon and I managed only to prove a weaker form of the conjecture; namely that backgrounds preserving a fraction ν > ¾ are locally homogeneous — a result collected in Supersymmetry and homogeneity of M-theory backgrounds.
In 2006-2007 I turned again to this issue, but now for ten-dimensional supergravity backgrounds. This was prompted in part through my rôle as external examiner for the thesis of Philipp Lohrmann, a student of George Papadopoulos's. The geometry of type I backgrounds is better understood chiefly because of the happy accident that the superconnection is induced from an affine metric connection with torsion, hence the possible holonomy groups are under control, being (intersections of) spinor isotropy subgroups of the spin group. This has now resulted in the classification of supersymmetric type I backgrounds. Trying to streamline some of the results in Lohrmann's thesis, I managed to prove the homogeneity conjecture for type I backgrounds borrowing my previous results on parallelisable heterotic backgrounds. Emily Hackett-Jones and George Moutsopoulos had been working on the similar construction for type II backgrounds, so we joined forces and wrote The Killing superalgebra of ten-dimensional supergravity backgrounds. This paper contains the construction of the Killing superalgebras for ten-dimensional supersymmetric backgrounds of types I, II and heterotic supergravities. It also proves the homogeneity conjecture for type I and heterotic backgrounds, whereas for type II backgrounds we are again only able to show that ν > ¾ implies homogeneity.
I still believe that the homogeneity conjecture is true, but proving it requires a better understanding of the holonomy of the superconnection. The relation between holonomy and symmetry, which has an illustrious pedigree in differential geometry, seems to be equally tantalising in supergravity.