Galaxies are classifed according to the Hubble Sequence, from Spiral (Barred and unbarred) to Elliptical. As well as ones which are neither of these called Irregulars. There is a nice description of this classification here, as well as a diagram.
Karen was a graduate student at Cornell from 2000-2005. She went on to work as a researcher in galaxy redshift surveys at Harvard University, and is now on the Faculty at the University of Portsmouth back in her home country of the UK. Her research lately has focused on using the morphology of galaxies to give clues to their formation and evolution. She is the Project Scientist for the Galaxy Zoo project.