Here are some amazing AJAX powered Web Services ranked as I like them. The list includes online word processor, spreadsheet, calendar, wiki and chat client.

TiddlyWiki - An amazing web application. It is "a reusable non-linear personal web notebook". In plain english it is a wiki which is contained in a single file, doesn't require any web browser and very usable and functional. I am using to maintain my TODO list. But you can do much more with it.

Writely - Online Word Processor; supports Word and HTML document.
The AJAX provides a fast writing and editing experience that makes it as slick as a desktop application. You can use it to blog too.

NumSum - Online Spreadsheet with ability to use formulas. Import from Excel via cut-n-paste.

Kiko - Sharable draggable event calendar; interactivity of a desktop calendar, with the added convenience of online access.

Meebo - Multi-colored AJAX powered chat client. It allows you to login to your favorite IM services and provides a MDI web client; pretty neat stuff.

Despite my ranking above I think each of them are amazing products in terms of usability and simply the jazz factor.

Thanks to MacMerc via MacManx for pointing me to these applications.