OK, per the suggestion in comments here, I decided to see just what it was that was filling up the /var partition. Here it is:

##########################################

[root@linux-station ~]# du -s /var/*
12 /var/account
773872 /var/cache
16 /var/crash
28 /var/db
16 /var/empty
60 /var/gdm
56716 /var/lib
8 /var/local
128 /var/lock
86208 /var/log
448 /var/lost+found
4 /var/mail
232 /var/named
8 /var/nis
8 /var/opt
8 /var/preserve
340 /var/run
72480 /var/spool
8 /var/tmp
8 /var/tux
13936 /var/www
24 /var/yp

#################################

I can live without the contents of cache, right?

Well, maybe not:

[root@linux-station ~]# du -s /var/cache/*
80 /var/cache/alchemist
472 /var/cache/gstreamer-0.8
1344 /var/cache/man
8 /var/cache/mod_proxy
8 /var/cache/mod_ssl
384 /var/cache/samba
771568 /var/cache/yum

#######################################

Note that it’s all cache/yum. Does that mean that if I blow it away, my ongoing yum upgrade gets clobbered? Getting rid of logs will help a little, but I suspect that the yum cache will quickly fill up the available space if I give it any. What now?