There is no limit on the number of messages for a mailbox but the recommended mailbox size limit for Tiger Mail is 2 GB.
19K messages in your Inbox - pardon me but WOW!!! and why so many unread messages? Did you not read all these messages or did the Mail.app mark these messages as unread again after being read? I'd be surprised if you have not experienced any problems with this mailbox in all this time.
Since an account's Inbox mailbox is usually the most active mailbox and more prone to corruption over time, it is not a good idea to use an account's Inbox mailbox as the final storage location for all received messages not deleted that you need to keep.
Better to create/utilize "On My Mac" location mailboxes to sort received messages by category and the same with the account's Sent mailbox.
There is a collection of AppleScripts called Mail Scripts you can download at this link.
http://homepage.mac.com/aamann/Mail_Scripts.html
The script to use from the collection of scripts is
Archive Messages (Mail) which moves messages from the selected mailbox(es) to an archive mailbox or export them to standard mbox, plain or rich text files for backup purposes or import into other applications. You can select to move all messages or only messages sent within or certain period as well filter messages based on their read and flagged status.