New Orleans is no more crime-infested than any other large city, which is probably contrary to what you may have heard.  The reason New Orleans is considered by some as a high crime city is two-fold. First, it's a big tourist attraction; hence there are a lot of "eyes" on what's happening there - more so than what happens in cities that aren't as big of tourist attractions.  Secondly, when many people visit New Orleans, they let down their guard somewhat…because of the large crowds. 

Some say, "There is safety in numbers."  And while this might be true to an extent, it doesn't mean you shouldn't take common-sense precautions.  In the highly unlikely event that you fall victim to a crime (usually pickpockets/muggers, but could be much worse), the only thing that's certain is you will NEVER catch or see the perpetrator again….ever.  While there's "safety" in huge crowds, there's also "anonymity."  If you are victimized, my recommendation is that you find the nearest police officer or a pay phone and call the police (immediately) - not that they will be able to do anything, though.  To possibly help prevent falling victim to a crime, see the tips below.

Don't bring valuables to Mardi Gras unless you absolutely have to; and if that be the case, store them in your hotel's safe.

Never show anyone your hotel room card folder or tell them your room number unless you know you can trust them (or can overtake them if something goes wrong).

Luggage

Never, ever leave your luggage unattended in public.   If you turn your back on your luggage while in a hotel lobby, airport or rail terminal, you could be the victim of an SNR (Snatch 'n' Run).  This happens no more in New Orleans than it does in other cities; however given the large number of people that will be coming in for Mardi Gras, thieves will be chomping at the bit.

Stupidity

Don't fall for the "I bet you money that I can tell you where you got your shoes" trick.  Note:  This isn't technically a crime because participation is subject to mutual agreement; however, don't participate unless you want to be out some $$.

Someone Following You

If you sense that you are being followed by someone suspicious, get yourself occupied. Occupation usually discourages following, and is also an excellent tactic for getting rid of drunks who won't leave you alone. Walk over and start talking to a cop if one happens to be around. If not, go into a restaurant or a bar and don't leave until you know your follower has left the area and the coast is clear. What if they follow you into the restaurant or bar? Make friends with someone there, and fast. Your follower will soon get lost (but make sure they aren't standing outside waiting for you).  In most all cases, the person following you is probably just drunk or interested in becoming friends with you, but you should always remain cautious.

Mugging and Other Crimes

The golden rule:  "For I say unto you, thou shalt not veer off the well-lit, beaten path; for whomsoever doth veer off this path shall assume a great risk."  Stay in well-lighted areas where other revelers are.  Do NOT wander into dark alleys anywhere or down streets beyond the edge of the French Quarter.   There are several rough neighborhoods within walking distance of the Quarter.   The most important Mardi Gras safety tip of all:  STAY ON THE BEATEN PATH.

Pick-Pockets

Pick-pockets love big crowds, especially at parades and other large, outdoor events.  The best way to guard against this crime is to carry only the important items you need, and carry them in places other than your pockets (or at least not in your back pockets).  One popular way to carry such things as money, credit cards, and other essentials is to purchase a small, leather bag that can be attached to your belt in the front.  I don't know the proper name for these bags, but they are very common.  In addition from being pick-pocket protection, these bags are also good for storing fragile items such as cameras.  You're less likely to bump something or get bumped in the front that you are in the side or rear.  There is also such a thing as a "money belt."  The concept is simple - carry your short-term spending money in your front pocket, and keep a larger amount in your money belt.  But watch out - smart criminals know which belts are "money belts," and might want to follow you to the restroom or some other area if they think you're about to replenish your supply of cash!