The first part is: know your audience. I just saw a version of this conversation with one of the web developers from The Economist, and his team isn't willing to push away any group that represents more than about 3% of the current audience. Their monthy page count comes to about 5-6 million, so pissing off 3% of the audience translates to roughly 175,000 angry people.
Next, ask yourself how closely does technology X correlate to your customer base? So your website demands Flash, for instance. Fine. That means you're tying yourself to a subset of Macromedia's deployed base. Do you have any numbers to show that your ideal customer is almost certainly in Macromedia's deployed base and almost certainly not outside it?
A sub-question of that is: what business are you really in? Are you trying to sell widgets, or do you make your money pushing Macromedia (Microsoft, Real, etc) products? If you don't get any checks from Macromedia (etc), does it make sense to turn away customers who don't use Macromedia (etc) products?
The next question is: what would the user have to give up if you didn't use technology X? If the answer is "code bloat, longer downloads, higher exposure to pop-under ads, viruses, etc, and a chance to have marketing's 'message' drummed into their eyes and ears," you might not be backing a winner.
The web is a pull-driven medium. It doesn't matter how much you like the site. What matters is how much the users like your site. All the corporate mandates and internal-political wrangling in the world are irrelevant when the user looks at your page. Users don't care about your agenda, they don't follow your corporate marching orders, and they don't have some yutz from department Z sitting over their shoulder saying the site must be this way. They come, they look, they leave. If you're lucky, they'll see something else to look at in the first 10 seconds or so. If not, you'll probably never see them again.
With those ideas in place, the best strategy I've seen is: gentle degradation. Go ahead and add any bells and whistles you want, as long as the site remains functional at a grey-pages-and-click-the-text-link level. That way, the people who don't have technology X can still use the site, but the people who do have technology X can appreciate the extra work you've put in.