Mexico City is a dangerous city. Do not wear jewellery. No gold earrings or gold chains. Wear a black, plastic watch only.
Mexico City is no more dangerous than any other big city. I believe that it is unhelpful to brand it as unsafe in this way for people visiting. Does murray2000 have direct experience to back up his statements? Or is this just sensationalist gossip that has been passed on to him? The only advice I would give to visitors is not to hail taxis on the street (especially the green VW beetles), but to use a taxi 'sitio' or to book one by phone. Otherwise, as Londontraveller says, Mexico City is a fantastic, vibrant, friendly place, and visitors should be allowed to enjoy its many attractions without being frightened off by this kind of scaremongering.
I'm from Mexico and there are some situations in which you should be careful. For example:Send your feedback or queries to been.there@guardian.co.uk
Search Been there
It is like any other city - you just need to be careful and aware.