If you want to blend in, dress like a local. For Americans this means, for example, no shorts. Wear linen trousers instead. You'd be amazed at how much better you're welcomed.
I feel about as safe in London and Paris as I do in LA
or San Francisco. Normal caution rules apply of course.
As for airports, security varies, but is generally on the same level as in the US.
My friend got pickpocketed in Rome. A 20 year old girl flashed him. He was of course pretty surpised, especially when he discovered that her friend had taken his wallet...
I once saw an Englishman at the Spanish Steps. He stepped out of a taxi and looked around. The taxi left, with his luggage. The naivete of some people...
[Edited 2004-04-22 15:43:29]
"There are no stupid questions, but there are a lot of inquisitive idiots." - John Ringo