What's the best way to upgrade from Django 0.96 to 1.0?
Although this depends on what you're doing, most applications should be able to just upgrade and then fix everything that breaks.  In my experience, the main things that I've had to fix after an upgrade are

Changes to some of the funky stuff with models, such as the syntax for following foreign keys.
A small set of template changes, most notably auto-escaping.
Anything that depends on the specific structure of Django's internals.  This shouldn't be an issue unless you're doing stuff like dynamically modifying Django internals to change their behavior in a way that's necessary/convenient for your project.

To summarize, unless you're doing a lot of really weird and/or complex stuff, a simple upgrade should be relatively painless and only require a few changes.
Should I try to actually upgrade my existing app, or just rewrite it mostly from scratch, saving what pieces (templates, etc) I can?