One of the easiest ways to avoid sticking out like a sore thumb in Europe is to blend in with the look. That means no American flag T-shirts, T-shirts in general (on women), socks with sandals (please), shorts, Yankees ball cap, fanny packs, Steelers jersey, hooded sweatshirts (nobody cares that you went to Columbia), running sneakers with jeans or flip flops. Your yoga outfit should stay in yoga class. Trade all of that in for something a little more European.
The first step is blue jeans; chances are you already have them. Second, Converse All-Stars or ballet flats on the feet during the spring or summer, and leather boots (above the jeans, please) during the winter. When in doubt, wear a scarf. This goes for both men and women. Heavy scarves in winter and lighter silk or cotton during the spring. Men: collars or polos, with either leather on the feet or Converse All-Stars. No Nike sneakers. Warmth for all genders: sweaters. Added warmth: wool button jackets. If you are young, anything H&M will suffice.
Generally when in public, keep your voice down. Particularly when riding public forms of transportation such as the metro. In most large European cities, the majority of metro riders are locals on their way to work; if you get in the way of a Parisian on the metro, they will undoubtedly be annoyed. If you get in the way of a Parisian on the metro and you are bellowing at your friends in English, then they will not only be annoyed but will probably glare at you. Keep your voice down; you may speak, but remember nobody else wants to hear. English is a dead give-away you are a tourist on vacation.
Avoid traveling through Europe in large groups, this goes for tour groups as well as huge family outings. Traveling in pairs, or even trios (such as a mom, dad and child) is much less conspicuous than a 20-person group in matching T-shirts and khakis gathered in front of Caesar's tomb. Aside from looking like tourists, large groups also have difficulties finding space in restaurants and cafes. Most restaurants in Europe suited for massive crowds are the tourist restaurants--the ones you should be trying to avoid in the first place.
Many Americans who are embarrassed by their heritage opt to adhere a Canadian flag pin or patch to their lapels, bags or backpacks to insinuate they are Canadian and not American. Do not do this. It will backfire; all Europeans know what you are trying to do. Chances are, if you are wearing a Canadian pin, you will automatically be taken as an American.
You want to avoid waving your foreignness like a flag, as it will be taken as conceit, but you do not need to be ashamed of your heritage. Be proud that you are the one experiencing new things, that you hold the courage enough to walk the streets of Barcelona, and that it is the Spaniard with the raised eyebrow who has not the courage enough to travel to your country. Instead of being a tourist when voyaging outside of your country, be a traveler.