When I started angel investing, staying stealth seemed to be partially in vogue. There were still a lot of entrepreneurs who wanted to stay stealth and they would ask me to sign an NDA before talking about their startup. Unfortunately, I can't sign NDAs in my business; if I did, I would quickly not be able to talk to anyone! But the world seemed to move to a more open working relationship and those who really wanted to stay completely stealth seemed to dwindle in face of the hordes of startups who didn't care.
Staying stealth was also a barrier to many startups working in the consumer space. At one time, if you could get on Techcrunch, you'd find yourself instantly with 100K users within a week and things would take off from there. You wanted to get out there as fast and as broadly as possible so that users would know about you and come and try you out. More importantly, there were not as many startups back then; thus, competition was always a danger but the rate at which competitors popped up seemed manageable.
Lately, though, I have found myself advising at least two recent startups to now stay stealth as long as possible. While their stealthness wasn't during the fund raising or development process, I thought it was now a bad idea to announce themselves to the organizations that cover or announce startups and is normally read by other current and near current entrepreneurs. This is because now the world has changed: it is much easier with today's tools to create a startup, and since so many people want to become entrepreneurs today, the likelihood of somebody just copying you is much higher than ever before. Internationally, there are already teams working solely with the aim of copying US based startups and launching them in their local countries.
Today, in my search for startups, I try always to work with startups with no or very few competitors; it's one of the most basic concepts for investment selection and in today's climate, it is back to being one of the most important. But given the ease at which competitors pop up, it now benefits a startup to keep from announcing themselves to other potential entrepreneurs for as long as possible so that you can get a headstart on your operations, customer acquisition, product development, and dominance. This is much easier if you don't have the typical 5-10 guys who seem to suddenly pop up every time a startup with a new idea gets funded (Or think Groupon, who has HUNDREDS of competitors).
My new word is: stay stealth for as long as possible to the places where other entrepreneurs tread often; go public only because you have to in order to gain customers and in those places which reach the general populace, which unfortunately does contain entrepreneurs but you can't really do anything about that.