Having lived in a large city in the States (Philadelphia), I have to say that the crime here in Madrid is no worse. Keep in mind that Madrid is Spain´s largest city and Capital. With a population of nearly 4 million in the city alone and 7 million in the entire autonomous community (including areas such as Majadahonda and including an estimate of those who are living here unregistered...empadronado), one has to expect crime....just as in any large city.
I used to live in a residential area of Philadelphia city (near St. Joseph´s University for those who know the area) and a friend´s car was stolen from in front of my house. My car had been broken into at least 3 times in the city and one day I awoke to find a bullet hole in the trunk of my car.
Here in Madrid, my car has been broken into and rendered useless as someone used it for their hotwiring experiment and failed miserably. However, for as much as I ride public transportation...at all hours of the day and night... I have yet to be pickpocketed.
I really don´t think that blowing the crime issue out of proportion is helpful. What is helpful is knowing that if you are not accostumed to big city environments, there are a few things you can do to keep your pickpocketing risk low:
1. be aware of your surroundings, particularly if someone is standing "too close for comfort". If you are on a jam packed metro, you won´t be able to move away, but at least be more aware of your belongings.
2. Know where you are going. Avoid "looking lost". If you have to consult a map (and believe me, I have lived here for 3 years and still do), try to do so from the safety of a bar while having coffee.
3. Carry only the absolute necessary on you in forms of documentation. Don´t carry the original of your passport. Carry a photocopy. Leave the original in your hotel safebox. Use your drivers´ license or other easily replaced document for a photo id.
4. When at internet cafés and bars/restaurants, do not leave your bags on the chair next to you, on the floor, or hanging on the back of your chair. Keep them on your lap if possible. If not, situate yourself and your belongings so that it would be next to impossible for someone to casually walk by and grab your bag.
5. Use your common sense. If you are uncomfortable with an area, avoid it. Stick to large well-lit streets at night if you aren´t familiar with the area. Stick to where there are crowds or populated streets.
6. Lastly, be aware but not paranoid. Nothing can ruin a trip faster than constantly being afraid of being robbed.
Violent crime risk here is very very low compared to the US.
Come and enjoy yourselves!