I try to dress down (or up as the case may be) to look less of a tourist, but the style of clothing itself is a dead giveaway. Clothes in Europe are just cut differently from the US so it's almost impossible.

I once went to Nordstroms and asked one of the consultants to dress me so I looked less like an American. She did a pretty good job from their stock. Although there were things she suggested that I just plain didn't like.

Another giveaway for travellers from the US is the Mediterranean peoples propensity to be all bundled up when it's a sunny, high 40 degrees day. They're wrapped in wool scarves and gloves, all zipped up, and we're walking around like it's a spring day. Hard to bundle up and swet for the sake of the goal. (I remember New Year's Day in Rome a couple of years ago when we were dying of the heat and the Italians were freezing.)

I agree with PTravel that the most important thing is not to look and act like the ugly American. That means quieter voices, more genteel manners, more than European fashions.
Rita