Oh boy...jury duty stories. I've never had to serve, but I do have a good one to share. Apologies in advance for the long post.
I was called for jury duty in San Francisco for the week of September 10, 2001. I called in on Sunday night and found out that I wasn't in the group to report on Monday. I called in again on Monday night to find out that I was supposed to arrive for duty at 9 AM on Tuesday, September 11. So I wake up the next morning at 7:30 (much earlier than usual for me at that time in my life), flip on the TV as I get breakfast ready, and see the World Trade Center in ruins. The country was of course in chaos as nobody yet knew the extent of the plot and whether there was more coming. There were runners on the bottom of the screen talking about government offices being closed, but I didn't see anything about the courts where I was headed.
So I hopped in my car (once I picked my jaw up off the floor, I was too late to take public transit and still make it) and drove down to the courts building on McAllister in the heart of SF's Civic Center. I get as far as Van Ness and it's total gridlock...streets closed off, cops everywhere, cars not knowing where to go. I finally found a traffic cop who told me that the courts were shut down, so I spent the next hour and a half trying to get home.
I believe that the courts were also closed the next day, but did have to report on Thursday the 13th. Once everyone was assembled in the waiting room, the judge arrived and informed us that the case we were being selected for was an industrial asbestos-related case that was expected to last at least six months, and possibly as long as a year.

Fortunately, I was able to plead my case as a grad student who would essentially be adding any research time missed due to jury duty service onto my already-long grad student career and was named in the very first group of excusees ("excusees"...not a word, but it should be).
My second jury duty summons came three weeks after I had moved out of San Francisco in 2004, so I got out of that one as well.