Dreamer, Dances gave you an excellent answer about what knife would be legal throughout the US. I'm not an attorney, but I've been researching the same question and have come up with a slightly more detailed answer. I'll post my summary below...
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Restrictions and blade length limits vary widely throughout the US, but posession of an under-3-inch-bladed (measured from end of handle) normal folding knife (including one-hand-opening locking folding knife) carried either concealed or openly should be legal almost everywhere. Avoid fixed-blade knives, double-edges, spring or gravity opening knives such as switchblades or balisongs (butterfly knife) or anything flickable. Normally prohibited in: schools, airport secure areas (inside checked luggage is OK), courthouses, federal buildings (2.5 inch exemption), and wherever posted.
Of course, it is illegal to brandish or threaten anyone with any knife. Since many jurisdictions ban *any* concealed "weapon," never refer to your knife or anything else as a "weapon;" only as a tool (LEO: "Do you have any weapons?" You: "No, but I have a pocket knife." LEO: "Why do you have it?" You: "Opening boxes." Do not say "self-protection." Say no more. Ask for attorney if questioning is incessant.).
These general guidelines should be OK in Canada and Mexico also. Check first before entering other countries. Laws change and enforcement could be more strict than law, so you can never be sure.
Notable exceptions to the above guidelines:
Ohio: Possibly more restrictive laws in certain cities such as Akron & Cuyahoga Falls which consider blade lengths greater than 2.5 inches to be weapons.
MA: The cities of Boston and Lynn have a 2.5 inch limit.
NY State: There may be a 16 year minimum age limit and you may have to be a US citizen there to carry any knife. In NYC, open carry is illegal, so concealement may be legally required. On a related note, posession of chemical mace is probably illegal in NY state.
California: 2.5 inch limit on all school property including all colleges/universities.
Following the 3 inch guideline above should allow you to travel freely throughout the US without having to worry about the local variations in law (note above exceptions). If you want to go beyond the 3" general guideline for folding pocket knives or carry a fixed-bladed knife (normally illegal to conceal), It is likely you can do that in many localities in the US, but you must research the laws for any localities you will be in to be sure of being in compliance. Applicable laws include state, municipal and possibly county and special regulations such as university policies and watch for different ways jurisdictions measure blade length, such as 3.5 inches from the pivot in CO, and also that concealment may be either prohibited or required. Penalties for violation can be severe in some cases including felony charges.