Plan 9 has an extra permission for files; "append." When set, this means programs are only allowed to append text to the end of the file. Both simplifying logging (just open the file and write) and making it more secure (no arbitrary writes.) I wonder if Lennart and Kay would accept a solution that simple...
Linux also has append-only files, although as usual root can override it.
# mv log log.old
mv: cannot move `log' to `log.old': Operation not permitted