Apart from petty theft, Barcelona is perfectly safe. Clueless tourists who leave their wallets in their pockets are asking to be pickpocketed (wear a neck pouch). The normal streetwise precautions apply (e.g. keep an eye on your belongings, have your wits about you, be observant, and don't look so blur!).
It isn't so hard to pick up a few Spanish phrases which will certainly help you to get around a lot easier. Don't just rely on English. Be a responsible tourist and learn a little of the local language. It will enhance your travelling experiences there.