Although BirdieSync has been heavily tested, it is strongly recommended to backup your data before installing a new version.
To regularly backup your data, for instance you can use MozBackup for your Thunderbird profiles.
Note that you can also simply backup your Thunderbird/Sunbird directories:
Thunderbird C:\Documents and Settings\[users name]\Application Data\Thunderbird\Profiles\
Sunbird C:\Documents and Settings\[user name]\Application Data\Mozilla\Sunbird\Profiles\
XP: C:\Documents and Settings\[users name]\Application Data\Thunderbird\Profiles\
Vista: C:\Users\[user name]\AppData\Roaming\Thunderbird\Profiles\
(Application Data is a hidden folder: in explorer window, you must check the option "Show hidden files and folders")
You can also use a free online backup service. Some of them offer to backup up to 2Go for free. That can be enough to backup very sensitive data.
To backup your mobile device, here are some examples of applications you may use: