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Files grow. It's a fact of life. There are log files in /var/log (they may be in /var/adm, or somewhere else, depending on your system). In my mail directory I have saved-messages, and sent-mail, and files for the various mailing lists I'm on. In my Chess directory, fics.pgn stores every game of chess I play online. Files in my News directory swell with my Usenet posts.
Most modern Unix systems offer a log rotation program that can be configured to suit many of your needs. Files can be rotated daily, weekly, monthly, or whenever they reach a certain size. They can be compressed or not, as you wish. Traditionally, log rotation files have been numbered, with the most recent always having a suffix of .0, the next oldest having .1, and so on. When a new rotation was performed, the files all had to be renamed. The one with the highest number would be deleted.