Ditto, watch out for pickpockets in Barcelona (well, all large cities in Spain) and also in Italy, particularly Rome. I nearly lost my wallet to a Gypsy pickpocket in Barcelona (she had it in her hand and I saw it and snatched it back from her), even though I had the wallet safely (I thought!) stowed in a kangaroo pouch that I was wearing around my waist, in front. However, this sort of thing has been the norm in Europe for who knows how many years; it is not an indication of terrorist activity.
If you wish to avoid anti-American comments and so forth, don't dress or act like a *sterotypical* American. Avoid white sneakers like the plague; wear only black sneakers or some sort of nice walking shoe. Do not wear sweats of any kind, short shorts, or too-casual clothing anywhere -- it just screams "American." No "gimme caps" or ball caps; wear a nice hat. Keep your voice modulated; assume the people around you can understand English. Basically, make sure you are wearing decent clothing at all times, at or maybe a little under the level of office-casual. We observed these rules, and people routinely assumed we were English and were quite surprised to find out we were American.
All this said, it's no reason to stay away from Europe if you have the chance to go! There are many great sights in Europe and it would be a shame to miss them.