Depends on your definition of 'safe' and the person doing the asking. I'm 1.82 and 120Kg so I don't get picked on that often.
Do you stand a chance of losing your wallet? Definitely yes, especially in the area of Las Ramblas, the Old Town area off to the left of Las Ramblas at night, and in the area of the Olympic Harbour of a night-time if out wandering the bars.
The usual trick was to try and drape arms around you like a long lost friend whilst shouting the name of an English football team very loudly. Left hand around your money and a large free hand to push off the attention seemed to work for me.
You are also likely to see gangs working the 'Find the Coin' routine on the Ramblas which is kind of fun to watch from a distance if you can spot the 'players' but less fun if you join the game - you will lose - and if you lose your wallet in the crowd of 'spectators'.
Crowds of young kids milling around near tourist metro stations are also a pretty good indication that you ought to keep your hand on your wallet.
The bottom end of the Ramblas also gets a fair cross section of 'ladies for hire' and associated street offerings late into the night but is pretty normal early evening and in the daytime.
That being said for all its petty stuff I have never felt unsafe in the city. The violence of other big cities seems absent.The cabs are cheap if you want to avoid walking of a night time and the usual rules about splitting up your cash, keep cards back in your room, carry ID, and keep your wits about you apply in Barcelona just as much as any other big city.
Still one of my favourite cities in Europe.