I usually shoot alone, if for no other reason than I tend to take my time and would rather not feel rushed or make others wait for me to fiddle with my camera. When out shooting, there are definitely times when I feel a little uneasy, depending on the neighborhood I am in or the time of day/night. At least here in Boston, though I assume it's true in many other cities too, with the prevalence of digital cameras in everyone pockets, and the speed with which a just-taken photograph can, within moments, end up on the web, it's not surprising that folks are wary of being photographed without consent. Anytime I am out shooting street scenes, I am cautious--probably far too cautious, in fact. Most people just ignore me when I'm photographing landscapes and things like that, though. They just think I'm some weirdo with an antique camera.
Shooting in Europe last summer, my concern was not for my personal safety, but rather that my gear would attract thieves and pickpockets. Regardless of where I am, though, I try not to flash my gear around. I don't switch lenses on the go much, and my film-loading speed with my mechanical cameras is glacial at best, so in those instances I usually go somewhere where both my gear and I are safe, rather than preoccupy myself and make myself a sitting duck for potential wrong-doers.
I don't know if it's a more dangerous world we live in now. I just think it's amplified more by 24-hour news coverage than ever before.