I know that IBM is referred to as Big Blue because of their blue logo (not
to mention their enormous size). When was that term coined and who first came
up with it?

Hello zpatch-ga, and thanks for an interesting and enjoyable question.

The first reference in print to IBM as "Big Blue" appears to be a June
8, 1981 article in Business Week magazine with the title "NO. 1's
AWESOME STRATEGY".  The phrase appears roughly midway through the
article:

"No company in the computer business inspires the loyalty that IBM
does, and the company has accomplished this with its almost legendary
customer service and support. Other computer makers, in fact, measure
their own service and support capabilities against what IBM provides.
As a result, it is not uncommon for customers to refuse to buy
equipment not made by IBM, even though it is often cheaper. "I don't
want to be saying I should have stuck with the 'Big Blue,' " says one
IBM loyalist. The nickname comes from the pervasiveness of IBM's blue
computers."


From the context, it appears that "Big Blue" may already have been in
colloquial use at the time.  But according to a search on LexisNexis,
this is the earliest use I could find of the term in print.  (Another
Business Week article in the 1970's referred to IBM as a "big blue
chip company", but that didn't quite qualify as a legitimate "big
blue" reference).

I hope this answers your question.  If you need any additional
information, don't hesitate to let me know through a Request for
Clarification, and I'll be happy to provide additional assistance.

Just what I was looking for.

Hello, zpatch-ga.

I was unable to turn up anything definitive on the subject.  No-one
seems to know where or exactly when the term originated.  It is
thought that it may have come about either due to the blue logo (as
you say) or because some of their early mainframes had blue cases. 
The closest I came to a date was early 1980's as stated in this FAQ by
IBM:

What is the origin of the term "Big Blue?"
http://www-1.ibm.com/ibm/history/reference/faq_0000000068.html

Sorry I couldn't help more.  Maybe someone else can turn something up.

Best regards,
bikerman

The staff used to wear blue suits as well...

Thanks so much for the stars anc the tip...always appreciated.

paf

Great answer, if I might say so. 

I searched the web, and found referrences to the name originating from
the colour of their system boxes (see for example
,http://groups.google.com/groups?q=%22the+name+big+blue%22&hl=en&lr=&ie=UTF-8&oe=UTF-8&selm=7fq76s%24rqr%40top.mitre.org&rnum=15>),
but no-one seemed to indicate to the first (printed) referrence.