Music & Pictures
Your music and pictures can be synced through zune so you have a backup there.
Contacts
You can store your contacts in your live account or exchange account. This way your contacts will always be synced through all your devices / computers
Connected contacts won't be stored anywhere
Apps
All the apps you bought/downloaded are stored by microsoft. On the windowsphone.com website you can see a list of all the apps you've installed before. There is an app called reinstaller that can help you reinstall all the apps in a quicker way than just browsing the marketplace searching for your app: Reinstaller
You can view a list of bought/downloaded apps on the WindowsPhone.com website here:
https://www.windowsphone.com/en-US/account
Your home screen tiles won't be backupped anywhere since this connected to your installed apps which aren't backupped aswell (only complete list of downloaded/bought apps available)
App data will also not be backupped.
SMS & Call History
Not possible at this moment
Settings
Not possible at this moment