NOTE about Concrete5.6 and up: I've moved this functionality over to github: https://github.com/jordanlev/c5_ajax_form/ and will no longer be maintaining this addon. It works fine in 5.6, but the github code works better, and I can't guarantee this addon will continue to work in 5.7, 5.8, etc.
This is a set of custom templates which add ajax functionality to the built-in form block, so that pages do not reload when forms are submitted.
To ajax-ify a form, simply add it as you normally would (or edit the page if it's already there), then click on the block and choose "Custom Template" from the popup menu, then select "Ajax Default Layout" from the dropdown menu and click "Update", then exit edit mode and publish your changes. Voila -- welcome to 2006!
If you are a designer or developer, there is an additional template called "Ajax Tableless Layout" which is completely unstyled but puts all of the form fields into divs (very similar to the Form Tableless Layout addon), so you can style them yourself via your theme's CSS.
If you're not a web designer or developer, you should completely ignore the "Ajax Tableless Layout" template and just stick to the "Ajax Default Layout" template, otherwise your forms will look weird.
Some notes for the detail-oriented folks: