[WanderingTraveler]

(This applies in any situation where your phone sustains a lot of damage, or you have to hard reset it. Now, moving on...)

Yes, you can. However, the backup system is quite limited.
You can back up:
1. Your apps
-As of Windows Phone 8 Update 3, you cannot backup app data if the app does not support it. However, it is rumored that Windows Phone 8.1 will support this natively.
-App data includes files, by the way.
2. Your messages
3. Your photos+videos
-Be warned that auto-upload to SkyDrive may cause Other Storage problems.
4. Your documents
-Save them to SkyDrive via the Office Hub and they'll be there.
5. Your contacts
-Link your Microsoft Account to your phone, and you'll be fine.

Settings for the first three are found in settings>backup
Your documents can be backed up by saving them to SkyDrive via the Office hub. You can also link it to an Office 365 account.
Contacts? People hub, or settings>email+accounts.

Anything else that I missed out on?

[DBDev]

Nice tutorial!