Summary:
watch the growth of files
xtail watches the growth of files. It's like running a tail -f on a bunch of files at once. My favorite usage is:
$ xtail /var/log/*
You can specify both filenames and directories on the command line. If you specify a directory, it watches all the files in that directory. It will notice when new files are created (and start watching them) or when old files are deleted (and stop watching them).
The xtail program has been around for a long time. O'Reilly & Associates even included it in their Unix Power Tools book. A link to the 1989 release is included below. The 3B2 sitting in your cellar would love a copy.
19 Feb 2012 Update - I've included patches (to the 2.1 release) from Jari Aalto below, as 20120219-patch-aalto.zip. I've not reviewed the patches. Jari's patches include a fix for SIGQUIT under Cygwin, as well as some Debian patches.