Hi lulu, Madrid is different from New York and Chicago since it is a Eurpoean city and a touristy one. The city center is usually pretty packed with visitors as are the more interesting Plazas and sights and the shear concentration of masses makes for a pickpockets paradise, especially in places like the
PUERTA DEL SOL and
EL RASTRO but don't worry, street smarts will come in handy.
Even better than street smarts is basic common sense which unfortunately many visitors either lack or just temporarily forget
As an example I can tell you that a few weeks ago a friend a friend of mine was here visiting Madrid and then went to Barcelona. She was having a drink at an outdoor terrace of a restaurant and put her backpack down on the ground behind her only to not find it there when she got up to leave
I always tell poeple that your backpac, pocket book, etc should become an extension of your being while you are abroad (not only in Spain). When eating at an outdoor terrace, in the
PLAZA MAYOR for example, you should wrap the backpack straps around your leg and put it under the table or tie it to the table leg. At the
RASTRO street market or in the
PUERTA DEL SOL or any other square, one should turn theri backpack around and have it in front of them as a "chestpack"

or hold their purse the same way. Also, in those areas do not keep valuables in front or rear pants pockets, that is just begging to have them "removed".
So, while one should not be paranoid, common sense is a must.
I also have some useful tips on safely changing money on my Money Matters section at
www.multimadrid.com/practical_info/spain_money.htm I am sure you will be fine.
Saludos,
jer...