Organists: What are some pieces that could be used as processionals for graduation.?

I always find that Bach works well for those sorts of situations. You could try one of his shorter preludes, something from the "8 Little Preludes and Fugues" might be nice. I believe there are also some nice Buxthehude toccatas you could do, or if the organ would allow it, Gigout's Grand Choeur Dialogue is always a good processional.