As far as I know, it isn't possible to directly sync Things with your Windows machine; sorry.
(The Mac <-> iPhone sync works quickly and reliably, so if you sync your iPhone with your Windows box, perhaps there's some way to get your notes to Windows, through the Notes app, maybe. But that wouldn't be automatic or very convenient really...)
The above is based on following their blog, and looking at their FAQ. Also, check this question about syncing the iPhone version with Outlook; quote:
A direct sync of to-dos between Things
on your iPhone and Outlook is
technically not possible at this time.
We hope that in the future Apple will
allow third parties to sync to-dos and
calendar events with MobileMe.
The only way to sync with Outlook
would be via a Windows version of
Things. But there is no Windows
version yet. We'd love to have Things
on Windows as well and will consider
this as we move forward.
Also, there's no sync with MobileMe or any such internet-based service available either, at this point. I guess for now you'd just have to wait for either Outlook sync or Windows version of Things. :-|
Personally I use Things avidly on my home MacBook and on iPhone, but when at work (using Linux/Windows), I just stick to the iPhone version. (For work-related TODOs I use other things than Things - our scrum tool or personal textfiles - except if ideas pop-up when I'm not at work and I want to write them down.)