As others have pointed out, it isn't a binary question of whether or not you support it, just to what extent. If you're considering going back to the Dark Ages of a "browser gate" where you disallow IE6 users, I would advise against that.
Salesforce.com, which caters exclusively to the business community, has chosen to drop IE6 support for new features.
Salesforce and Internet Explorer 6
Depending on the complexity of your site/application, IE6 support may not be all that difficult. Our HTML/CSS needs are basic, and as such we have a very small, conditionally-included IE6 stylesheet, included last, that tweaks the settings defined for FF3/IE7.
So before making your decision I would consider several things:
- What/who is my intended audience? A site like w3schools or stackoverflow stands a much better chance of having users who are on the latest browsers.
- What level of support is adequate? What (if any) features will IE6 users be missing out on? Can we gracefully degrade?
- How difficult will it be to support? A few CSS tweaks or an entirely separate set of templates? If you need 50 lines to have terrific IE6 support, why not?
It's all about balance :)
What I would advise against is making a soapbox stance, and I'm little concerned about the word "feeling" in your question. It's simply a business tradeoff, as the SF.com blogger pointed out - either you spend time creating more new features in FF3/IE7 more quickly, or you spend time getting those features working in IE6 (thus slowing down your delivery of new features).
I would also suggest choosing your statistics carefully. While the original response pointed to w3schools, it should be noted the audience there is highly technical and I'm surprised any of them are on IE6 at all.