I am searching for the names of the top 10 insurance companies that
provide coverage to Fortune 100 companies for their business
liability.  In particular, I am looking for the companies who have
been involved in financing the costs of litigation.  Most companies,
when they are sued, have coverage that pay the costs of outside
counsel and related expenses (expert witnesses, etc.)  This is not
something that all insurance companies deal with.

Which companies deal with large litigation coverage ($500,000 to $1
million annual costs and above)?
What type of coverage is most prominent?  Business liability?  D&O?  E&O?

The insurance coverage that comes into effect depends entirely on what
the suit is brought by.  The coverages that would most likely come
into effect are as follows.

1. General Liability
2. Errors & Omissions
3. Directors & Officers
4. Employers' Practices Liability Insurance (EPLI)
5. Professional Liability

The 5 above categories break down which type of claim the suit would
be.  For example, if someone is suing you because they fell on your
property, that would be a GL claim.  On the other hand, if an employee
is suing you for wrongful termination, that would be an EPLI claim. 
If one of the board members was misusing funds and it financially
burdened an employee who is now suing, that would be a D&O claim.  If
an accountant got sued for messing up someone's taxes, that would be a
Professional Liability claim.

To answer your specific question about which companies cover what, the
answer isn't that simple.  Different companies have different targeted
classes of business.  All of the larger insurance carriers will write
certain things and stay away from other things.  What is paid for by
an insurance company at the time of a covered loss is usually
determined by each individual company.  Some companies provide more
comprehensive coverage than others, but there is one thing to keep in
mind.  During a loss, all insurance companies will do what they can to
minimize their losses.  I am a little confused about the phrase "most
companies, when they are sued, have coverage that pay the costs of
outside counsel and related expenses (expert witnesses, etc.)" because
things like expert witnesses ARE part of your defense.  Insurance will
pay for whatever defense costs are associated with a covered loss.

One other thing to consider is that many of the larger companies that
you may be thinking of are part of captive insurance programs. 
Captive programs are a form of self-insurance, and can reduce costs
greatly.  When you're in a captive, or when you own your own captive,
you don't really have an insurance company per se.  Instead, you are
buying reinsurance directly from a reinsurance company.

I hope this helped a little bit.  If there's anything you want to
clarify about your question, I'd be more than happy to help the best I
can.