Things to avoidPick pockets
Beware: if you go to places that are full of tourists, there are thieves around. Don’t carry all of your money with you, and if you have to don’t put it all in your wallet or your bag. The most dangerous places in this respect are probably Puerta del Sol and the El Rastro flea market, but all overcrowded places are dangerous in this respect.
Just don’t go around with a city map open and your nose in the air, your 2000$ camera hanging from your neck, your Louis Vuitton bag full of cash hanging loosely and half-open at your side. Common precautions measures, also on public transport, should be more than enought, since Madrid is otherwise quite safe if compared to other cities of the same size.
Double decker buses
Instead of being a nice public means of transportation like in London, in Madrid they take you around to - almost - worthless tours for a minimum price of 10€. If you’re on a budget, with that sum you can go around on the Underground, see the places you really want to see and have money left to buy some food or a couple of drinks as well.