I have an '82 Brat that I picked up recently and started fixing up.  While I was replacing the struts I found that the sway bar connector on the passenger side was hanging.  I was considering removing the sway bar altogether and was curious if people run without front sway bars on Brats?  

i would like to know this as well

The only concern I see is if the suspension articulates too far it could cause damage to the CV joints...

i haven't driven without one. but a lot of people here have, mostly to squeeze a little benefit out of driving off road. When somebody asked why I ran the swaybar on my lifted hatch instead of going without, my answer was that i was afraid of a bad handling car handling even worse. Now that I've driven it around for a while I realize this car so rarely breaks 55 miles per hour that it probably wouldn't matter much. The bottom line is there is nothing wrong with taking it off and seeing how you like it without. Lots of folks here have, and the wheels don't fall off. I don't think doing so will buy enough articulation to damage you cv joints.