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If a regular backup is not performed or your email logs aren't clearing when they are supposed to they can build up and start filling up your hard drives. I suggest the following process as a quick fix to the problem.

In the EMC go to Organisation Configuration -> Mailbox -> Properties of Mailbox Store (private and/or public) and at the Maintenance tab enable circular loggin.
 
After that unmount and remount the store... (like the message suggests) this clears down all the current logs automatically.

Afterwards a full backup should be run for the reasons explained below. 

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Reason for full Backup:

You can configure Exchange to save disk space by enabling circular logging. Circular logging allows Exchange to overwrite transaction log files after the data that the log files contain is committed to the database. However, if circular logging is enabled, you can recover data only up until the last full backup. For example, you can enable circular logging when using Exchange Native Data Protection, in which you don't make backups. Therefore, to prevent log buildup, you need to enable circular logging.
 
In the standard transaction logging that is used by Exchange 2010, each database transaction is written to a log file and then to the database. When a log file reaches one megabyte (MB) in size, it is renamed and a new log file is created. Over time, this results in a set of log files. If Exchange stops unexpectedly, you can recover the transactions by replaying the data from these log files into the database. Circular logging overwrites and reuses the first log file after the data it contains has been written to the database.
 
In Exchange 2010, circular logging is disabled by default. By enabling it, you reduce drive storage space requirements. However, without a complete set of transaction log files, you cannot recover any data more recent than the last full backup. Therefore, in a normal production environment, circular logging is not recommended.
 
For information about how to enable and disable circular logging, see Configure Mailbox Database Properties. Found here: http://technet.microsoft.com/en-us/library/bb331958.aspx