Generally, yes. Spain is a hugely popular destination and most people who go there feel they can move around freely, enjoy themselves and come home with no problems. However, there are certain precautions you should take.

There is some street crime, and a lot of this is aimed at foreign visitors as they carry more money (this is typical for tourist destinations anywhere, of course). Be careful of your wallet and passport, starting from the airport. Also be wary if anyone comes up asking you a question in a crowded city - for instance, there have been cases of people pretending to be police officers and asking to 'check' your wallet.

All the recent financial troubles in Spain have caused worries that crime will rise, but it's too early to say whether this will happen and how much. Certainly, at present it is still fair to say that Spain is a safe destination in most ways, providing visitors use their common sense.