Hmmm, well just like Greg I've seen dating of this nature work out and not work out. I would be an example of it working out. My wife and I met while training. I wasn't an instructor (or even an assistant instructor) at the time. About a year after we started dating, I started my "assistant instructor" duties. Things have worked out well for us, we dated for about three years and were married last fall.
I've seen couples come to the dojo and start training together. One of them soon realizes that Aikido is not their thing, and decides to quit. Now, the relationship suffers. I've also met people who have come to the dojo in order to meet someone. Obviously an Aikido dojo is not the best place to meet someone; Everyone is dripping wet from sweat and constantly falling down.
Instructors dating students can be a very bad thing, especially if it does affect the training of other people in the dojo. As an instructor, you must remember that you are there to teach; and more than likely you are getting paid to do it, except for Greg
It is very important to maintain positive, professional relationships with all of your students otherwise the dojo will suffer.