There are a few initiatives in new technology (and some old) to help prevent bag theft.

There is some interesting information on http://www.karrysafe.com/. Here they talk about four different types of bag theft and how to protect against them.

Anti-slash: New Yorkers put chicken wire inside their handbag to avoid losing the contents if the bag is slashed.
Anti-dip: Use a small travel padlock to keep you zips together to help prevent pickpockets.
Anti-lift: Simply a padlock with a long wire to wrap around your bag and a table or chair.
Anti-grab: Use a personal alarm with a pull cord and attach the alarm to your bad and the cord to your wrist.

There are also some initiatives in research and design.

Research conducted in Korea during the development of an antitheft handbag by CNE Tech Co. Limited, a provider of patented alarm sensors, and the Esquire Collection Co. Limited. The companies worked together in order to develop a crime prevention alarm capable of being fitted into a handbag, thus protecting its owner from being a victim of pickpockets. The alarm was inserted into a stylish leather bag, chosen for its popularity with a range of customers and its supple/flexible material. Designed to go off when the surface of the bag was slashed, the alarm protected its owner from being the victim of bag-ripping, where a razorblade is used to cut a hole in the bag. The anti-theft bag has increased sales and significantly improved the company’s image.

Source: http://www.designagainstcrime.org/

There are several bag alarms available which involve two pieces – one in your handbag and one on you. Then when the bag (or you) is a certain distance away the alarm will sound. However currently these are very expensive and not widely available.

If you know of any great ideas regarding handbag theft or snatches, then please let me know.