Sure you can bring a knife camping.
Can you tell me a
other way of carving your name in those trees :P Getting serious,
when you travel around United States you must take into consideration the law,
which differ in various areas:
locking knives over 4`` are prohibited in New York City,
California prohibits all types of folding knives.
I personally recommend when going on camping trips to get a fixed-blade (hunting knife,
remember to wrap it good so you can conceal it in your camping gear (this is allowed).