The most substantial improvement in version 0.9 is, of course, recurring to-dos and projects. See below for an entire post describing this new feature.
Here is a list of some of the other improvements:
Choose Things Library
This is clearly an advanced feature that should be used with care. When holding down the option/alt key while opening Things, a dialog will be displayed that lets you either create a new Things library or choose an existing one. This feature is practically identical to a similar one in iTunes.
You can now store your library in a place that might be more convenient for your backup routine. Choosing a web-based location is not possible.
This feature is probably most interesting for people who would like to carry their Things library with them. Plug in a portable or USB flash drive and move your Things library from its default location Home/Library/Application Support/Cultured Code/ to that drive. Move the entire Things folder and don't forget to quit Things first! The next time you open Things, it will ask you for the new location.
Better error handling
Things will now catch more unexpected errors and also offers a convenient way to send reports via email. Due to some limitations in Tiger this feature works best on Leopard.
There is a new Duplicate menu command in the Edit menu.
The Postponed list is now called “Scheduled”. There are a couple of improvements here. Since the Scheduled list will be the home of our recurring item templates, “Postponed” no longer seemed appropriate. But more about this in the post below. Scheduled now uses relative dates and groups items under headings like “Next week”, “April”, etc.
Move to Today
When an item is postponed, there is an option to automatically move it to the Today list on the specified date.
There are also many bug fixes, some of them quite substantial. More details can be found in the Release Notes.