IE6: To support or not to support
It's not news for anyone, Internet Explorer does not support CSS standards. It's a pain to develop websites that work for all major browsers especially because IE6 is one of them (for now). Developing for IE6 means that you have to spend time to change the markup to make the website work and look the same way as with any other browser. That time is time not spent on adding features or making the code base more solid.
IE6 is also a dangerous browser to use. It has plenty of known security holes and is very vulnerable.
For and Against
Even though IE6 is about 8 years old (a lifetime on the Internet), a lot of people still use it (as of today - June 2nd - about 25% of Internet users) making it the third most used browser (behind IE7 and Firefox). The good news is that the number of IE6 users can only go down and it's dropping fast.
It's also important to know the demographic of the users visiting your website. I don't expect a lot of IE6 users visiting my blog because it's aimed at a more tech savvy audience. If you're designing a website for everyone from 7 to 77 then you should consider supporting IE6 (or at least make the features work, maybe you don't care if it looks ugly for them).
Of course, if you've been hired to develop a website by someone and they want you to support IE6, you don't have much choice. Though it's your job to inform them about the extra costs and development time, maybe this will make them choose otherwise.
People and companies won't stop using IE6 unless there's a reason for them to do so. Tell them about the security issues and the extra costs associated with using IE6. Tell them about alternatives or even install another browser for them. People are afraid of change, tell them they can have Firefox that looks the same as Internet Explorer so install Firefox, download the theme and change Firefox's icon for the IE6 icon. They won't notice the difference.