JavaScript is an incredibly powerful and expressive language; there's not a lot you can't do with it (especially in the HTML5 context -- the web workers, etc., that lemon-tree mentioned). It's my preferred language for server-side development as well (in the Rhino environment on the Java Virtual Machine, on the Jaxer server, in CouchDB) whenever it's available -- it does Lisp-y things using a syntax that doesn't play havoc with my emotional security.
That being said, one needs to be a little bit careful building a website that depends on JavaScript. If it's a web application, something that acts as a replacement for a desktop application or for a proprietary client/server application, you may be left with little choice. (Rich text editing, for instance, needs JavaScript in order to be WYSIWYG; without JS you are left with embedded codes like BBcode, Markdown, wiki markup or HTML, and need to wait for a round-trip to the server to see what you've done.)
If, on the other hand, you are running an information service or are involved in business-to-consumer activity (B2C), you need to create a site first that does everything it's supposed to do with JavaScript disabled. (Ideally, it should be completely usable with CSS disabled as well.) Once that is in place, you can "paint" enhanced behaviour onto the web page in order to provide additional features and make the user experience more pleasant. (I really have to write a progressive-enhancement tutorial at some point.)
Remember that if your site ever becomes successful, some portion of your user base (or at least of your potential user base) is either going to be disabled in some way (so usability and accessibility are key), are going to be behind corporate firewalls (and may have JS disabled by IT policy), are using "smart" phones that aren't so very bright at all, or will be ill-informed and paranoid (and will have JS turned off because they are afraid of what it might do). Those three groups can account for thirty percent or more of your potential users, depending on your target demographic. If you hope to make customers of these people (or even to gain ad revenue from them), you need to ensure that they can use your site even if it means a few extra clicks and a few extra trips to the server.