We have found it to generally be very safe BUT you do need to watch out for pickpockets! Keep all your valuables where they cannot be snatched and hold bags, rucksacks, etc. in front of you. As with any other city, night time and travelling alone when there are few people about can be risky so always stay alert and cautious.
Likewise, when it is very busy and there are crowds squashed together, this is a risky time for pickpocketing. Just be aware of your surroundings (as in any city).
Note that, although buskers are allowed in the stations, they are not permitted to busk on trains, nor are you permitted to give them any money.