There are enough warnings about pick-pockets and bag snatchers around the town that you really should be on your guard, but don't be paranoid. It's a safe city, and as long as you aren't stupidly flashing your money around you should be ok. There's almost no violent crime here either, so unless you go looking for trouble, you probably won't find any. I was walking around at all times of the day and night, and never felt uncomfortable, even outside the main tourist areas.
I personally didn't have any incident of pickpockets or bag snatching (not that I tend to carry a handbag!!!) but the centre of Tallinn has lots of signs around warning of the presence of pickpockets and Bag Snatchers. The places most likely to have lurking thieves is in and around the Viru Gates and Tammsaare Park near the Viru Centre. Like everywhere, take normal precautions. Like I said, didn't have any incidents but like everywhere, where there are tourists, there are pickpockets.
In the summer, when Tallinn is heaving with tourists, there is apparently a pickpocket problem - although I suspect this is no worse or no better than in any other country, although clearly the problem is serious enough to have warranted a sign being put up to remind tourists that the problem exists.
In 2004 I had a point & shoot digital camera taken out of a zipped up breast coatpocket at a large mall. The coat was on the back of my chair while I was sitting at the seat with four other people and we never got up and left the table once!!!! So don't think that the other warnings about pickpockets are just about ametures that "snatch & grab". I found out, after this happened that most of the pickpocketers and thieves move to the shopping malls(Kriistine and now Viru in particular) during the winter months. Kriistine is also one of the busiest places in Estonia for auto breakins and stolen auto's.
Like in any tourist attraction in a large city, the Old Town has its share of pickpockets. Immediately after our wedding reception, one of our friends was walking out of Olde Hansa restaurant when he was approached be a few guys. The men started being a it too friendly, talking to him and asking a lot of questions. One of the group grabbed the bottom of his pants and when he bent over to remove the guy's hand, another member of the group grabbed his wallet out of his back pocket. The "team" immediately began to run away and get lost within the crowd of tourists within the Old Town. Lesson learned - keep your wallet in your front pocket.
Originally I would have told you that the city is safer than most that I have been to in the past. Two females wandering around the Old Town on foot, using the tram for only one round trip to Kadriorg, had no problems at all. Admittedly anything of great value was locked in the safe in our room, but I never felt any concerns at all.
On the other hand, we met up with a Spanish friend who had his credit cards stolen on public transport from the pockets in his trousers (not his back pocket which is an obvious choice for thieves). So yes, you really do have to be careful.
I never had any problems in Tallinn, touch wood, but many locals have warned me that muggings and especially pickpocketing and bag snatching do happen, even to them, especially around the tourist areas.
Also, not a great idea to be wandering around drunk alone late at night.