MS Outlook has a tool called personal folder backup. when we install this tool it will backup the .PST files to the destination location automatically.

Is there any way to backup the emclient?

Yes you can. The default folder location for the database:
C:\Users\%Current User%\AppData\Roaming\eM Client (Vista/Win7)
C:\Documents and Settings\%Current User%\Application Data\eM Client (XP)

You can also use export (menu File->Export) for your emails, contacts, events and tasks.
Backup will be one of the large new features in next major version (or one of its updates).