in my experience both men and women are safe to walk alone at about anytime, although i would use caution when strolling alone through Gran Via, Vallecas, or Campamento at 3am. invariably, if you are in Madrid for as long as a week or more, you will need to walk at night because it is so easy to get around Madrid on foot, and the pleasant aspect of the city demands it. on a regular basis i have walked from around metro stop Tirso de Molina (Blueline 1 north of Atocha station) to the Arguelles-Moncloa neighborhood near the (Greyline 6) Guzmán el Bueno stop and never had problems. i have even passed huge groups of drunks that never even looked at me, so i have always felt very safe in Madrid.

the only crime i have ever heard about that was acted upon my friend was when he was on crutches for having hurt himself in futbol and he was on Calle Princesa, right over from Plaza de España in front of the Corte Inglés. a couple of chorizos asked him for all his money or they would beat him up. and he was alone and on the crutches so he had no choice, otherwise he could have run and they never would have cought him.

all in all i think you are very safe in Madrid, just be careful in club areas late at night and alone. keep in mind that the people of Spain, in general, are very kind and willing to help you if you are lost. you could probably ask a random man to help you and he would. just remember that there are also "gentuza," or bad people too.

good luck and have a lot of fun in my beloved Madrid!