This also works with destinations. My wife, who is Chinese, grew up in Beijing and is a fluent Mandarin speaker, will frequently have to call the restaurant or other destination that we're headed to and hand the phone to the taxi driver so he can get directions.

If you're traveling with a non-Mandarin speaker, always carry a hotel name card (the concierge or the desk will give you one) -- these say, in Chinese, "Please take me to: [name and address of hotel]." The concierge will also write down the name and address of the destination -- many hotels have special cards for this purpose. At the better hotels, the doorman will confirm with the taxi driver that he knows the destination before letting you get in. Also, you should know that the government has greatly improved the ring roads and the major boulevards as part of its preparation for the Olympics. Frequently, you'll find yourself in a "can't get there from here" situation as a result -- to get somewhere, your taxi may need to go in the opposite direction for a while, or navigate a complicated series of switchbacks. You're not getting ridden around -- it's really the only way to get to some places from some other places.

English is taught in the Chinese schools from elementary school on. However, as with many things, some Chinese are better students than others. Many Beijingers will try to speak a few words of English to you, but with varying degrees of success. I'd recommend learning a few simple phrases, with the caveat that Mandarin is a fiendishly difficult language to pronounce, being tonal and using a phoneme set completely different from English. Because of the traffic in Beijing and the way the streets are laid out, taxi drivers will, frequently, get you near your destination, rather than dropping you off right at it. Just stop anyone on the street and say the following (this is not Pinyin, the formal system for transliteration of Mandarin, but the closest approximation I can come up with for English speakers):

"Doo a boo chi, ching juan: [Name of destination] t'sigh nahr?" (The "a" is a long a, as in "day")

This means, "Excuse me, please: Where is [Name of destination]?" If you don't know the name of the destination in Chinese, pointing to a picture of it in a guidebook will suffice.

Saying, "thank you," in English will be understood by most everyone. It's just a personal thing, but the way most foreigners pronounce "thank you" in Mandarin sounds flat and unpleasant to me.

You don't need to worry about talking to strangers, except around major tourist destinations. As others have noted, there are common tourist scams, but none of them involve violence and, if they're done well, you probably won't even know you were scammed. Just avoid the pretty girls who want to practice their English and then invite you to tea, and the "art students" who want to show you their gallery or school. The one exception to this is the occasional beggar who can get very aggressive -- they'll try to hang on to your sleeve (they're saying, "Please, give me money!"). If you ignore them, they'll eventually move on. If you like, you can give them a couple of 1 RMB coins, but I wouldn't suggest it as it just encourages their colleagues.

At the Forbidden City, you can rent a headset that will guide you around in English, so you don't need any of the numerous "guides" that will approach you (though they'll do so very politely and almost always take a polite, "no thank you" without argument).

If you find a taxi driver and taxi that you like (almost all of the taxis in Beijing are brand new, but there are still some of the old red bone shakers around), use the hotel doorman to negotiate a daily rate if you like. Also note that most cab rides in Beijing will be very cheap -- 10 RMB when the flag drops and, unless you're going to the outlying areas of the city, rarely more than 20 RMB. At current exchange rates, this is between $1.30 and $2.50. Taxi drivers aren't tipped in China, though if you hire one for the day or negotiate a flat rate to the airport and the driver is helpful (gets you a cart, helps you with your bags, etc.) a modest tip is appropriate and appreciated.