I am a very frequent Manila visitor for the past years, never experienced any problems. The important thing here is indeed common sense. When visiting Manila, be on the lookout for petty crime, just as you would / should when visiting any other big city in the world.

During daytime, most areas are safe, especially the common tourist areas and places. Generally malls, transport and public places are safe. You will notice yourself the huge presence of security staff. At night you better not wander around beyond the 'international' areas like Makati. Even internationally oriented nightlife spots can become tricky but again, that is no different to any other big city.

Kidnapping foreigners is not a common problem in Manila. Kidnappings do take place in other parts of the county like Mindanao, where muslim rebels battle the government, these rebels are not active in Manila.

As Smkuchta said, the Philippines are still a 3rd world country. When you drive around the better areas of Manila, you might think differently but it is just a facade. There is a growing middle class in the country but unfortunately the reality is that the vast majority of Filipino live in extreme poverty. It is important to keep that in mind when visiting. Those few thousand pesos in your wallet often represent more than what the average Filipino can make in a month, so even though people in the Philippines are generally warm, friendly and welcoming, the temptation to have you 'share' some of your money with them is often strong.