Generally speaking Mallorca is a very safe place for tourists. Like anywhere else in the world occasional problems occur, but these are rare. Petty theft and `pickpòckets are the main problems but are mainly isolated occurrences.
In daylight there are no streets on the island I would not walk, and at nights normal care, i.e. avoiding dark backstreets particularly in Palma, keeping handbags tightly held and general care should see you alright.
Avoid the flower sellers near the cathedral in Palma, they are pickpockets.
Come to Mallorca it really is a very safe place about 8 years ago
Completely agree with everything that Peter has said. Mallorca is generally a very safe place even when travelling alone. As he says, as long as you take sensible precautions as you would in any towns or cities then you should have no problems. about 8 years ago