While I advocate keeping your stuff where you can see it, there are definitely times when that is not an option. As L.Wolf and others have said the main problem is in towns and Damascus definitely claims to be that.
Baltimore Jack also says to keep your valuables with you (IE - your ID, any money, your camera and such.). The rest bury in your pack deeply so that the person who might go rifling thru your stuff is discouraged of finding anything they can use.
For the most part the local sheriff/police are on site and providing security to Tent City. There are also many Trail Angels who stay in Tent City throughout the day. Mala, Preacher, Bill of Billville, Ms. Janet and Baltimore Jack attended last year. In general there are enough people around the campsites that few people are going to really bother your stuff without being noticed by someone. So just like being at home you should get to know your neighbors. If you have someone coming to visit who is coming via automobile then locking valuables in the car is also an option to be considered.
While generally everything can be replaced, give some clear thought to what is important. ID, Credit/Debit Cards, Ipods, camerasand especially money should be kept safe. No one but the most destitute is going to want your dirty smelly clothes, shoes, sleeping bag, tent or hammock so they may be safe to leave behind while you walk around.
Last year I had the advantage of having driven to TDZ so I had that security as fleeting as it may be. This year I will be one of the hikers, the good news is that I made the acquaintance of a few of the people listed above and feel relatively safe in leaving my stuff out or with them around.
As always be safe and be smart. If in doubt, don't leave anything behind or move to a safer location. Money can to some extent be replaced but not as easily as clothes. Use your intuition or street smarts to guide you on the correct approach when the time comes.
But then hey what do I know? You can ask LW or BJ or Ms. J!
Oh by the way Tent City in general hums and parties until the wee hours of the morning so if you really expect to get much sleep it will come between the hours of 4 AM and 9 AM. If you have a problem with noisy environments then you might want to consider one of the B&B's in town (expensive to say the least).
Really TDZ is an experience that you won't soon forget one way or the other. It's a time to meet current hikers, past hikers and future hikers, hostel owners (Ms J and Cloud 9 were present last year) along the trail and trail maintainers, Trail legends and some truly interesting people in general. You can be a part of the fun or you can people watch which can be just as much fun at times.
Lastly for those so interested, either VA or Damascus in particular have a law about visibly carrying an open alcholic beverage in public. So if you are so inclined remember that you need to stealth drink. Paperbags or Nalgenes generally work to skirt the law. In Tent City the cops don't go out of their way to look for it, in the city is another issue entirely. I guess every year that several people get stupid and end up on the wrong side of the law.