Take a look at TSA's site http://www.tsa.gov/311/index.shtm
They say you can bring a reasonable amount of juices that exceeds the normal 100ml limit and that the juice can be outside of the 1 liter 3-1-1 bag.
I wouldn't take fresh fruit. It would have to go in the 3-1-1 bag and that would get it confiscated because you're not allowed to take fruit into the US.
Any kind of crackers and cookies are fine. I usually buy a bottle of water after I clear security to take on the plane.
I bow down to Bavaria and Crashbb's superior knowledge.
I must admit I was thinking of oranges when I wrote about fruit. I'm amazed that an orange which is mostly liquid doesn't get handled like other liquids.