There is an algorithm due to Zassenhaus which, in principle, lists all conjugacy classes of finite subgroups of compact Lie groups.  I believe that the algorithm was used for $\mathrm{SO}(n)$ for at least $n=6$ if not higher.  I believe it is expensive to run, which means that in practice it is only useful for low dimension.

Independent of this algorithm, there is some work on $\mathrm{SU}(n)$ from the physics community motivated by elementary particle physics and more modern considerations of the use of orbifolds in the gauge/gravity correspondence.

The case of $\mathrm{SU}(3)$ was done in the mid 1960s and is contained in the paper [Finite and Disconnected Subgroups of SU(3) and their Application to the Elementary-Particle Spectrum][1] by Fairbairn, Fulton and Klink.  For the case of $\mathrm{SU}(4)$ there is a more recent paper [A Monograph on the Classification of the Discrete Subgroups of SU(4)][2] by Hanany and He, and references therein.


  [1]: http://link.aip.org/link/?JMAPAQ/5/1038/1
  [2]: http://arxiv.org/abs/hep-th/9905212