Apart from turning the computer off, ripping out the drives, and taking a peek firsthand? That, after all, is not an option. The servers probably shouldn't be down if not entirely necessary.

I run SuSE 8.2 on three of these machines, Red Hat on two, and SuSE 7.3 on the last. Any advice?

Go into /proc/ide/ and have a look around.

Here is /proc/ide/hda for instance...
:/proc/ide/hda$ ls -l

total 0
-r--r--r-- 1 root root 0 Apr 13 11:57 cache
-r--r--r-- 1 root root 0 Apr 13 11:57 capacity
-r--r--r-- 1 root root 0 Apr 13 11:57 driver
-r--r--r-- 1 root root 0 Apr 13 11:57 geometry
-r-------- 1 root root 0 Apr 13 11:57 identify
-r--r--r-- 1 root root 0 Apr 13 11:57 media
-r--r--r-- 1 root root 0 Apr 13 11:57 model
-rw------- 1 root root 0 Apr 13 11:57 settings
-r-------- 1 root root 0 Apr 13 11:57 smart_thresholds
-r-------- 1 root root 0 Apr 13 11:57 smart_values

All of your answers will come from these files.

you could use hdparm -i /dev/hda to get the model number of the drive (then google the model number for more details).

dmesg|grep hda

Thanks a bunch everyone! The assorted tips did just the trick, and I got all the information I needed.