You should follow "progressive enhancement" -- provide the core features of the site to most if not all users; then, for the A-Grade browsers, provide the additional eye candy and features. With IE6 still being used by anywhere from 10 - 20% of web users, we can't ignore it completely.
However, we can follow the pattern of Youtube and Google: display a message telling the user to upgrade. If you go to YouTube on IE6, you can't even view any videos anymore. This is what you'll see:
YouTube
And here's Google Docs on IE6:
Google Docs
