In terms of crime, Beijing is probably one of the safest cities of comparable size anywhere in the world.  In fact, it is so safe that people may let their guard down and expose themselves to being robbed or worse.  It is best to avoid wandering into isolated areas alone and it is important to keep valuables and bags secure at all times. 

Occasionally, there have been reports of people being robbed on remote parts of the Great Wall. Such incidents are rare--hundreds of tourists visit these sites daily without incident, but it is best to be cautious.   

Pickpocketing occurs in Beijing, though foreigners do not seem to be targeted in particular.  It is important to secure belongs before entering crowded areas or before taking buses or the subway.  It is also important to keep bags secure in restaurants. 

Stock Lots of Bottled Water

From the minute you check in to your hotel room, you will see signs everywhere warning, "Do not drink water from faucet."  Water is not drinkable in China, period.  Assume that during your entire trip.  Most hotels stock bottled water for you daily for free in your hotel room.  (Just don't grab the ones in the mini-bar)  And buying them at a nearby corner store will cost you very little money.  Bring them everywhere you go; your tour bus, on your tour, train trips etc...  You will not regret it.

Scams

Scams are increasingly a problem in China.  Most recently, people have reported being approached by young women who converse with them and then invite them to a teahouse.  There they talk, drink tea, and eat snacks, and a tea ceremony may be offered, apparently for free.  Upon leaving, however, the tourist is presented with an outrageous bill for the tea and snacks and pressured to pay.  

It is not common for people to be approached by people offering taxi cabs in the airport. However, this can happen around tourist sites. These people often display official looking tags, but they take people to unmetered taxis and try to overcharge for the trip.  Always be highly cautious if you decide to take a tricycle rickshaw or motorised tuk-tuk anywhere. They give the impression that your fare is cheap only to later demand an outrageous amount.  The best option, even for very short journeys, is always a legitimate taxi.

People posing as art students also approach tourists, mostly around Wangfujing.  They take people to see shows of mediocre, overpriced art and may pressure tourists to buy the paintings. 

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You may be approched by beggers or see beggers with small children on the street. These are sometimes run by large underground networks that take kids from villages, then put them on the street to beg. Sometimes these underground operations even physically deform a child in the hope of generating more sympathy money. So don't feed this negative cycle by giving them money. 

On the same note be prepared to be approached by dozens of street vendors or "side" vendors offering hats, t-shirts, etc...  If you are prepared and are completely serious about not buying, a slight shake of the head and a polite "no" or "no thank you" will suffice.  Alternatively, simply ignore them completely - don't let your own 'good manners' get the better of you. Keep walking to your destination and they will get the hint.  NOTE:  If you stop to even look or ask "how much?"  you will be most likely find yourself  surrounded (mobbed?)  by dozens of other nearby vendors.

Terrorism

People who live in Beijing usually consider Beijing to be safer than almost anywhere else, but Uygur separatists set off a small bomb in a Beijing bus during the 1990’s, and the U.S. Department of State does sometimes issue warnings of potential threats to locations in Beijing.  The State Department website provides information about these threats. 

Traffic and Bicycle Safety

The biggest real threat to visitors is probably accidents.  So people do not generally wear seatbelts in China, even though drivers are legally required to wear them.  Taxi drivers may act offended if you wear a seatbelt in their cab, and may say that they are not needed at low speeds around town.  Nonetheless, serious accidents are possible. 

Beijing is booming with new car owners every day.  And right now there are cars, trucks, bikes, mopeds, and pedestrians all trying to share the same road.  The driving in China have no real "organization" to it.  You practially see a mess of everything trying to share the road.  If you're from America/Canada  or Europe you will see the most scariest driving environment possible; no real rules and even stoplights are disobeyed frequently.   As a pedestrian it is VERY dangerous if you are not careful and you have to be hyper-aware of your surroundings.  Taxi's will literally try to drive through you to get to their destinations.

Likewise, people do not wear bike helmets in China.  They generally ride at low speeds, which is advisable, because construction, open manholes and other obstructions are common and often not marked or roped off in any way. 

Emergency response is not highly developed, so extra caution is advisable.   

Public Restrooms

Because of the upcoming 2008 Olympics Beijing is trying really hard to update and upgrade their restrooms.  In fact, many have a "star" rating to let you know how good the facility is.  The more "stars", like say, a "4-star" bathroom, have at least 2 "American" style toilets, per bathroom.  But they still have a long way to go.  Bring LOTS of extra toilet paper or tissue paper with you on your tours.  You will be surpised to find that once in your stall and doing your duty, you'll come to find that there's no toilet paper in your stall!  For most major tourist destinations this will be more of a problem than places like hotels and airports.

Yes, be ready to use the "earth toilets".  If you are not familiar, look it up.  There is no 100% guarantee that you will find a restroom area with an "American style" toilet.

Bring Hand Sanitizer

To add to the bathroom note above, people highly suggest bringing little Purell/Portable Hand Sanitizers along as well.  You can also use travel sanitary/baby wipes.  You might find yourself without soap and washing with just water.  It goes a long way knowing that you can have them with you anywhere in case you touch anything you don't trust.