The above posts sadden me as it shows how misinformed some people can be. I am from the Philippines and now live in the Midwest (for 3 years). I went to Manila for medical school. I'll try to be objective :-)
Preface: It's over 7000 islands, and each one can be different.
1. Manila is the least safe place in Luzon (main island), mainly because it is the biggest city, but it is waaaaay safer than Detroit, East LA, or Harlem. We do not have drive by shootings. Guns are nowhere near as commons as here in the US. People would rather buy food. That said, knives are more common (hehehe), but again, read the first sentence..
2. I agree with the common sense above (of course!) which would be applicable ANYWHERE. You wouldn't want to flash any bling in a poor country, and that goes for any country. It would offend the nice folks and attract the bad folks. And stay away from certain places and parts of town (duh!, there's always a ghetto everywhere), and probably stick to touristy places. A guide is always a good idea, 1. so you won't get lost, and 2. much less likely that anyone would mess with you, again, I refer you to #1. :-)
3. Remember that the people you meet on the street don't know you're American. If you're white, they assume you are :-). I wouldn't expect you to be singled out for being American, as FIlipinos actually like Americans (Expect a hey Joe greeting in every city, hehehe). Remember that American GIs were there from 1910s (although that was a bad time, lol) to 1992 (shall we say WWII to 1992 to keep out the bad memories). yes we do have anti Bush and anti war rallies (they have them in Kansas City, too), mainly by students.
4. The Abu Sayaff is listed by the US and Philipine governement as a terrorist group. It is a fundamentalist, separatist Muslim group in the Southern Islands, ade famous by a beheading of an American missionary several years back. At that time, they went as far north as Palawan ( a very beautiful place, I've been there once and plan to visit again). Some say they may have elements in Manila, but as far as I know, they have dwindled in number (the Philipipnes got a lot of help from the US government in fighting them since 9/11.
5. So in summary, No, most people do not carry guns in Luzon. Americans may be targeted by the Abu Sayaff, but historically, they are more of a kidnap for ransom group based on the opposite end of the country and that have dwindled in number. Outside Manila, you should feel safe moving around even by yourself in public transport, but a guide would be a good idea to help you find your way around, help you haggle with prices, even to shoo away vendors and malicious people.
Last words: Let me know if you have any questions, and do read the rest of the blogs and stuff to see how beautiful a country it is and how nice the people really are.