Some operators have a backup service the phonebook. But of course, paid each month. If you want a free and capable then can use the facilities of Google Sync. But of course must have a Google account and the phone supports synchronization feature. Most Nokia phones already have this feature. Google actually offers SyncML to sync and online backup Google Contacts to Symbian smartphones for free. But for Contacts only. Not for Calendar. It pulls all Google Contacts with all details including contacts notes and thumbnails.
With sync facility, a list of contacts in the phonebook are synchronized into the Google contacts list. Data contacts in Google also will be synchronized into the phone. Therefore you should create a new Google account specifically designated for backup phonebook if it does not want the phone contacts data mixed with a contact at Google.
Here are the instruction sync and online backup Google Contacts to Symbian^3 devices via SyncML, which is also can be used for older Symbian^1 devices (But there maybe some changes in the interface here and there and some functions may not be available in the older devices).
1. In your Symbian^3 samrtphones, go to Settings – Connectivity, and select Data Transfer.
2. Inside Data Transfer, select Sync.
3. Press Options, and select New Sync Profile.
4. Then, select Start.
5. Give a name to this new profile, Google or (You can put whatever name that you desire. Something that can be understood easily).
6. In Server Version, select 1.2.
7. In this one, select Contacts only. The other options are irrelevant.
8. In Contacts database, type contacts (please type EXACTLY like shown in the screenshot. No CAPITAL letters).
9. for Data bearer, select Internet.
10. Host address. Type exactly like shown : https://m.google.com/syncml. Note the https.
11. In Server ID, type Google. Use capital “G”.
12. Username. Your Google username. It’s your full Gmail or Google Apps email address.
13. Password. It’s self explanatory… anyway, your Gmail / Google Apps password.
14. Now, your new SyncML profile has been created. Press Yes to activate it.
15. You will be brought back to the main Sync page. Now, you can configure to sync automatically. If you prefer, you can also sync manually. If you want automatic sync, press Options and select Automatic Sync.
16. In here, define which sync profile and data that you want to use as automatic, as well as the sync interval and the time to sync automatically.
17. You can also choose to sync manually.
18. When it is synching, you can see a little sync icon at the notification bar.
19. It is also possible to view the log after successful synchronisation.
20. This is a notification of the next scheduled synchronisation.

Thanks for the great post. For Calendar sync, there's an app called GoogaSync that works fine on Symbian^3, even supports multiple calendars and all. http://www.googasync.com