Since the title of this thread says non-World Series, I would have to say the best White Sox moment would be Harold Baines Sac-File to clinch the division title in 1983. I can still hear Lorn Brown's radio PBP of that moment. Also Bo Jackson's home run after hip replacement surgery, would be right up there.
Worst, we have all seen some bad ones so I can't really think of one.
The funniest moment would be when Steve Lyons dropped his pants.