It really depends on what I'm building.. with certain kinds of web app it's not possible to deliver the kind of experience or functionality that users expect without JS, so I just consider JS to be a requirement to use the app (much like desktop software has requirements).
For websites in general though I'm a big believer in progressive enhancement - the site should still be functional without JS, but you provide an enhanced experience to those whose browsers support it.
Always, I wouldn't feel very professional if I didn't.
"Progressive Enhancement" is not a new idea.
Same with HTML, images and CSS
- the "raw" markup is still readable even without images or style
- pages without style are still usable
- pages without images still make sense
The HTML is the "foundation", all else just helps to make it better.
I agree with fretburner and Mittineague.
Also, a similar subject was discussed in some length recently.
The thread might be worth a read.