One of the unanswered questions of post-revolution Egypt is how unsafe things became. (Update: see how seuciryt looms large in this op-ed by David Ignatius) In the first days of the uprising, as police released common criminals back onto the street and carried out looting themselves, it was clear that security was low. Most of it could be ascribed to action by the security forces themselves. But as that particular problem subsided, and other issues came up.
The collapse of the police state meant that crime was no longer regulated (I tend to see the police as mafia dons who ensured that criminal activity was channeled and was not disruptive to public peace, much like drug kingpins might avoid violence among their ranks to remain below the radar — fans of The Wire will know what I'm talking about). In all likelihood, you had gangs who were no longer limited in what they could do that took matters into their own hands, as well as police officers involved in crime who simply switched sides. You also had, and continue to have, a demoralized police force that often does not want to do its job.
That being said, Egypt is still relatively safe. Not as safe as it used to be, but far safer than many Latin American countries, for instance. There are carjacks in certain areas, and a few cases of kidnappings of upper-class kids, but it's not chaos. It's not even US levels of criminality (which are quite high, mind you). Yet security regularly tops the concerns of Egyptians in polls, is a major talking point of the government and politicians, and even an argument by some for the postponment of the coming parliamentary elections. Some of this, I feel, is because the increase in security issues — even if small if compared to many other third world countries — is already a huge qualitative difference in the way Egyptians perceive their country. Mubarak's police state, through its regulation of crime and ubiquitous police state, kept things seemingly very safe. The same can be said of Syria I'm sure.
A recent Gallup poll has interesting data showing that while Egyptians worry more about security, they also report fewer incidents. Take a look at the charts below