In general, people think that if a policeman is nearby nothing bad can possibly happen to them, but in Mexico this doesn't really hold true and it can sometimes be the opposite: they're the ones who will try to take money away from you! Some authorities have been found out to be allied with criminals and participated in kidnappings.
DON'T be so sure that a cop will protect you. It's better to take your own precautions than relying on the cops. However, I do have to admit that lately the security has been reinforced in the city, more policemen are watching the streets on their patrols and some of them have actually been helpful to foreigners: I've had tourists telling me personally about their own experiences and they were grateful towards some police officers that were really kind & helpful to them in a moment of need..... this is rather uncommon but I was glad to hear that the situation might be improving!!
Also, if you'll be driving in Mexico City be respectful of the rules: there are many policemen out there trying to bust you disrespecting the traffic signs, permitted parking spots or speed limits so they can either get you to bribe them or give you a heavy ticket!
It's very handy and smart to actually learn at least enough of the language to make your way gracefully in which ever country you decide to occupy for however long. A little booklet which will help in any case, even if you are fluent, is this one: The Wordless Travel Book.
by Jonathan Meader, my first trip down to Mexico, my girlfriend of that time, had one of these and I witnessed just how handy it was. All you have to do is point at the little cartoon of which ever item or thing you want. It's not too hard to understand at all.
You'll be happy you did.
I have to say that I felt surprisingly safe in Mexico City. All the things I was warned about (muggings, dangerous taxis, food poisoning) turned out to be non-issues. Ironically, the only problem I had in the city was when I was approached by an infamous American con artist who tries to manipulate sympathetic tourists out of their hard-earned money!
This guy has actually worked all over Mexico, so beware no matter where you are. His story is always the same: He works for PriceWaterhouse in the states and in Mexico on business. Today is the day he is going to fly home (it's his son's birthday and they want to have a family dinner) but he left his passport in the taxi. Could you lend him a map so that he can get the emergency contact information from it? At this point he'll ask you to wait a minute while he calls Tourist Information, the taxi company, American Airlines, whoever. This takes up quite a bit of your time, which is why I walked away at this point, wishing him well and reminding him of how to get to the American Embassy. If I'd stuck around, he would have told me that because he'd already checked his bags American Airlines will allow him to fly, but only if he buys a new ticket. As ID is needed to buy a new ticket, he needs someone to come to the airport and show their ID. At the airport, something will go wrong and he'll ask you to front the money for his ticket, promising that Price Waterhouse will pay you back immediately. Apparently, people actually a) stick around this long and b) fall for it!
While your physical safety probably isn't at risk, your financial safety is. You can read more about this infamous con artist at the link below, and if he happens to approach you while you're in Mexico I suggest you just walk away.
The hardest thing about traveling in Mexico City is keeping your feet clean while you frolic all over the city in your flip-flops. Mexico City isn't the cleanest place in the world, and as anyone who read "My Flip Flops Almost Killed Me" in UK Cosmo a few years back knows, clean feet can be the difference between life and death. So, what can you do to stay clean and safe while navigating the mean streets of Mexico City? Consider carrying some travel wipes (available in the baby care section at most pharmacies back home) in your bag for on-the-go freshness. When you get back to your hostel or hotel at night, do a double-scrub: Put a good foot scrub (I swear by the Peppermint Plum one made by Freemans at the link below- it is way better than more expensive brands) on an exfoliating pumice stone and scrub away. Follow with foot lotion to prevent cracked heels (trust me, it will take weeks for the dirt to come out once it gets stuck in a crack). Keep some bandaids in your purse for random blisters (but don't be shocked if you buy Mexican bandaids and find the cushiony bit is brown... it's a cultural thing) and enjoy the lovely weather that allows you to wear sandals year-round!
It all has been said many times, theft, robberies, pickpockets, it all happens in Mexico city, so you have to be very carefull.
Don't walk alone at night, if avoided don't walk with a afew peoiple at night. Watch your belonging o crowded places, there are pickers there, and don't just take any cab on the streets, they are known not to be safe (most are, but don't take the change).
I am not sure if I should put this here or in the cultural tip place. The thing that shocked me most of all when I came to Mexico City was the poverty. Not in all parts of the city by any means, but it shocked me (and even shamed me) to see mother's with tiny babies sleeping on the streets at night. BUT whatever their circumstances they were ALWAYS so clean and the children were beautiful. I could not help but be so sad but full of admirtation for them.
I must sadly admit that my city isn't a safe one, and you must be careful while touring it in order not to have a bad experience on security issues. There's a lot of crime here, especially people trying to take your money away, so you must be cautious when walking around the city and using the public transportation system.
NEVER EVER have your money visible or count it in public, but I'm not talking only about your wallet here. Try to put away ANY stuff that could attract others' attention, such as watches, jewelery, expensive cameras, etc. You should hide this as well as possible, and not even take it out from your hotel unless it's necessary. Never carry important documents - such as your passport - with you, and try to carry as little money as possible and only one credit card (if you can avoid this too, better for you). Try to appear confident while moving around the city, even if you're not quite sure where you are, cause some people might try to take advantage of your being disoriented in order to take something away from you.
About public transportation: not only buses and metro are dangerous, taxi cabs can be as well. There are some unauthorized taxi drivers who charge you higher fees (they tamper with the meter) or even assault you, so it's safer to take taxis from fixed terminals (called SITIOS) that you can find near the shopping centers, metro/bus stations, touristic sites, etc. They may be a little more expensive, but they're safer. When going out at night you should double your precautions, stay away from metro and buses (the become even more dangerous at late nite) and try not to walk on lonely dark streets. Don't go to public parks at night. One more thing: policemen aren't that reliable -- although that has changed a little bit over time. Please read next tip for further info on this regards.
If you looks like a tourist, and normally you will do, don't take a taxi in front of the hotel. It could be very dangerous!
In fact, the danger level of this city is very high (compared with my city level in Spain, and the normal level in west Europe).
The time I spent in Mexico City was all clear blue skies but you could see pollution in the air whenever you looked off into the distance. For me, my eyes started burning and nose starting running after the first half day. It wasn’t as bad in doors in the hotel, but walking around the streets was irritable. I had run into a couple from Europe who had been to Mexico City the week before me with no ill affects, so obviously the air affects each person differently.
Mexico City's average elevation is 2,240 meters above sea level (about 7,200 feet). The city is high enough in altitude to cause problems in travelers such as shortness of breath, fatigue, loss of appetite or nausea. Be extremely careful if you have asthma, respiratory problems or other medical conditions which can be aggravated by this condition.
When I was in Mexico City there were police everywhere and had no trouble with any kind of crime. But, I’ve heard lots of horror stories. Like any other big city, there is crime in Mexico City. I suggest carrying only the things you really need. Carry a small amount of cash and hide any valuables that you may have on you. When going out on the town travel in groups and always be aware of your surroundings.