I have a list of company names all in upper case; one per line.
  Can I use a combination of sed, tr, and other tools to automate
  converting them all to mixed case (i.e., initial letter uppercase,
  all others lower case)? There must be a shell script already
  written to do this, but not in the reference books I have.

##</code><code>##

   perl -ne 'print ucfirst lc;' FILENAME
   will do it.

##</code><code>##

   perl -pe 'tr/A-Z/a-z/; s/(\S+)/\u$1/g;' <filename>

##</code><code>##

   My sed-fu was deficient I guess (or my sed was) so I fell back to perl:

   If you want word-case
   perl -pe 's/ \b (\w) ([^\s]+) \b /\1\L\2/gx'

   # ONE COMPANY  -> One Company (rather than One company)

##</code><code>##

   perl -i -ne 's/(\b\w)/{uc $1}/eg; print;' <FILENAME>