To change which list Siri puts new reminders on if you don't specify one, head over to the Settings app.
Reminders settings are, confusingly enough, found in the Mail, Contacts, Calendars section of the Settings app. You get only two options: Sync and Default List. Sync determines how far back your reminders are synced. You can choose to sync reminders from two weeks to six months back, or to sync all reminders. The default value is a single month.
Default List determines which list new reminders that you add outside of the Reminders app will go to. In truth, however, at this writing we're not aware of anything that this setting affects other that reminders you add with Siri, when you don't specify a specific list to put them on as you speak.
Reminders in the cloud
As we've covered before, you can set up shared lists in Reminders using iCloud. To set up a shared list, you need to go back to the iCloud website. When other folks accept your shared list, anyone can add, delete, or check off reminders on that list; the full instructions are in the linked story.
Shared lists are a big help for certain kinds of lists. You and your significant other might choose to create a shared shopping list; that way, you can each add items to the shared list, and whoever hits the supermarket first can check off any purchased items.
Even if you don't end up creating a shared list, iCloud syncing for Reminders includes an added benefit: If you use multiple iOS devices, iCloud keeps your reminders in sync on every iPhone, iPad, and iPod touch you use.
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