What are the top three to five existing DOS or other legacy software
applications in terms of the largest number of current business PC
users in US domestic and worldwide? (What software, who makes it?)
How many business PC users are currently using each of the top three
applications in US domestic? Need reference source(s).

My guess:

DOS is owned exclusivly by Microsoft - user numbers would vary
depending on what you actually mean (if you wanna X-fer me a check for
$50 I'll figure it out - but i'm not an "expert") especially since win
3.11, 95, and 98 run on it and have an option to boot to it.
 
VAX (still consule baised as far as I know) - HP (also free from
freeBSD) Used by military and by DuPont Pharma (now BMS) when I worked
for them and probably still by some other companies (once again - I'm
saving ya $50)

Unix - IBM probably shipped the most copys as Solaris, though they are
moving to a unix variant and also sort of a legacy OS called linux or
more properly GNU/linux.  So I would guess that HP or SUN probalby
ship the most now.

As for sources - try the "companymentioned".com and see if you can get
any exact info

(no wonder I'm unemployed as a biochemist)

WordPerfect 5.1 would probably be #1 on the list.  A surprisingly
large part of the legal profession runs on WP5.1 because it works, has
the right features and, once you've learned how to use it, is vastly
more efficient than Word.

As to numbers 2-5, I haven't a clue.

MS DOS is owned by Microsoft.  PCDOS isn't.  FREEDOS isn't.  DR DOS
isn't.

Unix hardly qualifies as legacy.  It's old, but still actively
supported, improved, etc. by companies with way more money than
Microsoft, and unices have features Microsoft could only dream of
(logical partitioning, resource allocation / prioritization, etc.). 
Solaris is Sun's Unix which scales incredibly well (Sun specializes in
huge systems with slow(er) CPUs and massive interconnect bandwidth). 
IBM's unix is AIX which runs on their POWER series of CPUs.  IBM's
Intel-based products (and recently its workstations and POWER-based
mainframes) run Linux which is also far from legacy - it supported
large volumes and files, as well as the LBA48 extensions for hard
drives > 128GB, AMD's X86_64 architecture, and many others long before
Windows did.

I know nothing about VAX.

I doubt this is anything like the answer you're looking for, but I
would suggest that technically the top three applications still
running under MS-DOS are as follows:

1. Windows 95
2. Windows 3.11
3. Windows 3.1

While Microsoft no longer supports any of these 'operating systems',
they are all still widely used. As much as Windows 95 is and was
touted as an 'operating system' it is still technically a software
program running under DOS.