This isn’t a new trick – and you could probably use the same technique to push reminders to any CalDAV-compliant system, but the folks at to-do list makers RememberTheMilk have gotten reminders to pop up automatically online.
The trick is to add RememberTheMilk as a CalDAV account. In Settings, select Mail, Contacts, Calendars. Add a new Calendar and enter rememberthemilk.com into the server field. Then type in your login and password. Then add RememberTheMilk to your default accounts.
Now, when you create a reminder, the iPhone will push the reminder to RememberTheMilk and store it locally. It’s one way to skirt Apple’s current controls over the Siri API although its usefulness is fairly limited right now.