I did some research on this log file, asl.log, and it turns out that some other programs can result in huge output to asl.log. For instance, Adobe Acrobat, see
http://www.24help.info/adobe-acrobat...e-6.html?pp=10
This link also includes an example of how the terminal command call to syslog can be used to shrink the size of the log file. However this requires using root privileges (sudo), but if one mistypes or makes mistakes when doing this, it could have unpleasant consequences. So it's probably not something that the typical user (like me) wants to do routinely.
The normal cron maintenance routines should eventually prune these log files, I have read, but when I look inside the "daily" script it looks like it does this only after 21 days, during which literally hundreds (or thousands) of megabytes might be piling up. I was getting 18 Megabytes in asl.log with each backup.
By the way, is this happening only on my computer, or have you or others confirmed that this asl.log file under Tiger (I was using 10.4.4) grows by as much as many megabytes with each execution of SuperDuper (my disk being backed up is ~ 20 Gigagbytes in size)? My OS has never been modified except through the Apple Software Updates, it's version 10.4.4 right now. Recall that the asl.log file is in a hidden directory, /private/var/log.