They are designed to understand the audience you are targeting. If your site is a lot useful without javascript, then it might be worth the extra effort to make a reasonable experience when javascript is disabled. You will need to understand the functionality of your site and the target audience to find out if this is an extra effort or not. There is no single correct answer.
If your site is not very useful when javascript is disabled, then you may not need to make an extra effort to try and do something other than telling users that javascript is required. Why invest a ton of extra effort (and a lot of extra testing) if these viewers are not loyal to your site and will be regular visitors, as the user interface will be quite undesirable.
So, the answer is: it depends on what your site is doing, who your competition is and who your audience is. Although people at SO love to argue with me in this regard (from the purity of every website they should work for everyone - I think), it is getting harder and harder to justify a business example for the extra work to create many sites without javascript these days. This, of course, depends on the specifics of your site, competitors and viewers. In my book, this in no way means that you must make each site work without javascript enabled.
If you are Google, you can find articles that discuss how many users have turned off Javascript. This mid-2010 Yahoo article article says they saw .25% - 2% of users with JS disabled.
As for Ajax specifically, there is no replacement or replacement without Javascript. If you have a design that depends on using Ajax to communicate with your server, then this design will require a Javascript period. The only alternative would be to create a non-Ajax design (a more traditional page request from your server with one URL for one static page), which can be used instead, which Ajax did not use. If your other design was used and depended on Ajax, this design without Ajax would be a significantly different design and implementation.