Where on the web can I determine what major clients a law firm have?
Or put another way, how can I see what lawfirms service what major
clients? I know that I can find the accountant for a public company
from Edgar or the SEC filings. What free sources of information will
work for law firms?

while most client information is, of course, private and confidential,
attorneys and law firms are able to make public a representative
listing of clients with the permission of the client.  the best known
and most easily accessible listings are found in the
Martindale-Hubbell directories.  Martindale-Hubbell directories are
published annually, are usually available at public libraries
[reference room] and have a biographical and firm information section.
 the firm's info will show the name & address, etc., of the firm, the
general areas of law in which its attorneys practice, and should list
some representative clients [corporate, of course - you will not find
individual persons listed].  martindale-hubbell has a website for
locating attorneys:  http://www.lawyers.com/

i hope this is helpful.

In addition to lawyers.com, Martindale-Hubbell offers a second
interface, which I prefer:
http://www.martindale.com/