The worst website is probably Turkmenistan Airways. Of the Big 6 US majors, Delta probably has the worst website, a rather ugly affair that's not at all enjoyable to use. US Airways also has an ugly website, but it's also very easy to use and US Airways has been progressively updating its functionality. Hopefully when their finances get in order they'll be able to give it a visual redesign that is more harmonious with their branding. I'd say AA
has the best website of the Big 6, with jetBlue probably having the best website overall.
The best website of any airline I've seen is, frustratingly enough, that of Air Canada. JAL also has a rather enjoyable website.