Edit: this potential 3rd way was confusing, and upon trying it myself I found that it didn't work. So it's going away
However, I did discover one interesting thing while playing around with this - for me my cdrom device isn't actually /dev/hdc, it's ide-scsi emulation so it's actually /dev/sr0 (I discovered this when I was trying to mount /mnt/cdrom, and the system complained about my filesystem type. It was nice enough to suggest that perhaps I ought to be using /dev/sda or /dev/sr0. sda didn't work any better, so that only left sr0!) So I deleted the symlink /dev/cdrom and re-linked it to /dev/sr0:
[me@localhost ~]$ ls -l /dev/cdrom
lrwxrwxrwx 1 root cdrom 8 2005-05-19 00:34 /dev/cdrom -> /dev/sr0
And that, plus the change from 'owner' to 'user' in /etc/fstab, means that mounting the drive as a normal user actually works
and gives me files ^_^
[me@localhost ~]$ mount /mnt/cdrom
[me@localhost ~]$ ls /mnt/cdrom
ANNOUNCE.10_0 COPYRIGHT.TXT GPG-KEY SPEAK_INSTALL.TXT kernels
BOOTING.TXT CRYPTO_NOTICE.TXT PACKAGES.TXT Slackware-HOWTO rootdisks
CHECKSUMS.md5 ChangeLog.txt README.TXT UPGRADE.TXT slackware
CHECKSUMS.md5.asc FAQ.TXT RELEASE_NOTES bootdisks
COPYING FILELIST.TXT SPEAKUP_DOCS.TXT isolinux
[me@localhost ~]$
Hopefully some of this is useful