The last three nights of our "Historical Central Cuba" tour took us to La Habana. As we entered the once prosperous city, our guide briefed us on it's history before and after the revolution. There are many buildings being refurbished now, and you'll see scaffolding and fencing everywhere. The buildings that have been repaired are truly spectacular with their pillars, high ceilings, tile and artwork.
Our guide encouraged us to explore Old Havana during our free time, and told us multiple times how safe the city is. That being said, off we went.
Cathryn and I had been there before, so we headed out to find a Bake Shop that made great little Guayaba turnovers. One turnover and a coffee made for a great afternoon snack. We returned to the Hotel Telegrafo in time to get cleaned up and head down for Happy Hour.
Turned out Happy Hour wasn't so great. One member of our group had her purse stolen by an athlete who specialize in "snatch and run". She lost her Passport, Drivers Licence, Credit Cards, and all her money. The poor sole, traumatized as it was, now had to endure a marathon session with the Cuban Police in order to get a report which would in turn, allow for the issuing of documents to temporarily replace her Passport. During the process, a number of different Police officers told the woman and her witness (through our guide/interpreter) that this had never happened before.
The next day I was having a Cristol (great Cuban Beer) at the Hotel Bar and a man from Germany sat down next to me. We exchanged travel stories. He told me how he was swarmed in a bar by a group of young women who left him without his money or his iPhone. He fortunately, carried only enough money for the day. The balance of his money, Passport and other documents were in the hotel safe.

So, is Havana safe? I'd say yes. We never once felt threatened when walking around, and have never heard of anyone being physically abused or mugged. However, where there are people, there are thieves. Practice good habits so as not to become a target. Stick to the main avenues. Use a bag/purse with a strap that can go over your head and shoulder. Carry the bag under your arm. Avoid flashing or counting large amounts of money in public. If you don't have a safe at the hotel, use a concealed money belt for your valuables. Always be aware of your surroundings. Seeing the same stranger nearby more than once on a busy street probably isn't a coincidence.
This was a very unfortunate event for our travel companion to experience. The lesson we learned from it is to never get complacent. This could happen in any city, in any country. Travel smart, be safe, and enjoy your travels.