Is there a utility, similar to chkdsk, that can be used to check the
integrity of a CD-ROM? I would like to make sure that all files and
directories on the CD-ROM are readable and that the disk is
properly closed/finalized. My Easy CD Creator hangs at the end of the
finalize stage and I would like to know if the disk is usable. Also,
I would like to verify that my backups are good before I delete the
files from my system.

View to CD through Windoze explorer, if you can see the files and can copy them back to your HD then the disc is good.

That is the obvious method, but with a stack of CD-ROMs, it can be
quite a bit of work. I seem to remember back in the old DOS days
that someone had created a "CHKCD" program that would work on
CD-ROMs. I am also concerned that the disk be "perfect" and not just
readable by my system. I have come across disks that would read on
one PC, but not on others that were not as forgiving about glitches in
the format of the disk. I need this for backups, so data security is
paramount.

If you use Nero, the Nero Toolkit has a utility called Nero CD Speed which can perform a Scandisk which give you the option of doing a file system check as well as a disc surface scan. The tool also performs may other CD related tests including media quality tests, DAE tests as well as read and write tests for the drives.
If you don't use Nero, the tool is available as a free doenload from CD Speed 2000 (http://www.cdspeed2000.com/).

Another good tool is Cdcheck, from http://elpros.si/CDCheck :)