My girlfriend and I (both in our mid/late 20's) recently spent 10 days visiting Barcelona, and I just felt the need to share my opinion on the many concerns of others over traveling to this city. I started reading the travel forum before I arrived, and became increasingly paranoid, for lack of a better word, about the economy, riots, protests, pick pockets, robbery, etc. I have done quite a bit of travel, so I knew that my concerns were probably just me over-thinking things. It turns out that I really had zero reason for concern.
We both took the proper precautions that any traveller should take, such as keep track of your valuables and put them in zippered pockets or in the hotel safe, pay attention to the people around you, etc. We stayed in Hotel Espana the first half of our trip (great for the money), which is just a block or two into the Raval neighborhood. We spent the first two nights walking around aimlessly through Raval, eating and drinking and had some great food, etc. We took main streets and dark alleys and did not once get approached by anyone selling drugs, prostitutes or anyone threatening at all. Given, some of the people in the area may look a bit sketchy, but I surely would not consider this to be a dangerous area, and would certainly encourage everyone to visit, just for a drink at least, as it is a unique area. I figured out we walked well over half of the entire neighborhood over two evenings. Barri Gotic was also an area that we spent much time in, and it also felt safe, although since it is the most touristy area of town I certainly paid a little more attention to my wallet, but again, there were zero problems (nor did we see anyone having any), and ate some truely great food. We spent the rest of our time visiting museums and all of Gaudi's work in various other parts of town. If you didnt listen to the news, you would never know what the unemployment rate is, as people seem to work very hard, and we didn't run into anyone angrily discussing the economy or blaming the government for things. So, to be clear, in my opinion, the economy will have zero affect on traveling to Barcelona.
Basically, I worked myself into thinking that when we went to Barcelona we were going to get pick pocketed, robbed, etc. But we didnt, and I felt as though this is important for others thinking of traveling to this truely wonderful city, as just take proper precautions like anywhere else, and you will be perfectly fine and enjoy your trip!