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To commemorate the 2,000th question on the English Language & Usage stack, I would like to actually know the origin of that word, and whether it originated for the negativity of the "end of the world" or otherwise.

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I'm not sure if it's apocryphal, but there is this article on Slate regarding the etymology of Y2K:

Y2K was born on Monday, June 12, 1995, at 11:31 p.m. It was delivered in the middle of an otherwise unintelligible e-mail, a contribution to an Internet discussion group of computer geeks exploring the millennium bug long before most people were surfing the World Wide Web.

The efficiency of the term is undeniable--"Y" for "year," the number "2," and "K" for "thousand" (from the Greek "kilo")--and it eventually caught on. But its creator remained unidentified until just over a year ago, when someone performed the equivalent of a computer paternity test by searching the discussion group's archives for the term's first use.

The father of the phrase is a 52-year-old Massachusetts programmer named David Eddy, who's now the president of a Y2K consulting business (click here to visit his Web page). "People were calling it Year 2000, CDC [Century Date Change], Faddle [Faulty Date Logic]," Eddy says. "There were other contenders. [Y2K] just came off my fingertips."

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Everything I could find attributes the term Y2K to this same guy. –  Kosmonaut Dec 31 '10 at 18:56
    
That is actually a good article and covered what I was looking for -- thanks! –  BeemerGuy Dec 31 '10 at 23:06
    
ghoppe @Kosmonaut: I found an earlier Y2K, but used in a variable name to fix a year 2000 bug. I couldn't find anything else earlier than Eddy's "Y2K". See my answer. –  Hugo Oct 30 '11 at 22:41
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Y2K stands for "the year 2000." This was the year all the ancient computer systems were supposed to crash because they couldn't handle 4-digit years. This was called the Y2K bug, and because of it banks were supposed to fail, airliners to fall out of the sky, and the digital world to come to a messy and somewhat ignominious end. But for a couple of digits the world could have been saved!

In fact the world went blithely on about its business. Reports of its impending demise were, in the words of Mark Twain, "an exaggeration."

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To clarify the abbreviation, in case it isn't obvious, k is the SI abbreviation for kilo, a prefix denoting 1000. So Y = year, 2K = 2,000. –  ghoppe Dec 31 '10 at 18:23
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Note that the world went about its business only because nearly every important piece of software had this bug fixed (partly because of the hysteria, even). –  ShreevatsaR Dec 31 '10 at 19:23
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More specifically, many programs were written to only use the last 2 digits of the year, e.g. "81" rather than "1981". The problems happen when computing things like interest over time - after Y2K, you end up with negative values: 01 - 81 = -80, and you can't compute a valid interest rate or other values over a negative time. Some of us spent a lot of time fixing these problems. –  Shannon Nelson Dec 31 '10 at 19:43
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The world did not go "blithely on about its business." In fact, millions of dollars and countless hours were spent reviewing and updating computer code, or outright replacing equipment which was not cost-effective to fix. A perfect example of people recognizing a problem and fixing it, rather than sticking their heads in the sand and pretending it doesn't exist. –  Mark Oct 31 '11 at 10:31
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David Eddy used the term Y2K on 12th June 1995 on Peter de Jager's Year 2000 mailing list. (Unfortunately I've not been able to find a copy of the original email.)

I found an antedating on Usenet, but as part of a variable, posted by Bob Brown to comp.lang.cobol on 2nd May 1995:

Newsgroups: comp.lang.cobol
From: MBGF...@prodigy.com (Bob Brown)
Date: 1995/05/02
Subject: Re: Year 2000

I've been working on this problem for a while now. The most popular
solution seems to be changing procedure rather than file conversions. The
problem with file conversion is that all programs using files being
converted must be completed at the same time. With procedure only,
programs can be converted individually. Two problems with this: 1) when
the date is part of a sort 2). when the date is part of an index or key
to a file. In both of these you must do a file conversion.

I will change procedure as follows:

If effective-date > expiration-date (I work for an insurance company)
move xyz to abc.

Change to:
call "convert-year" using effective-date, ws-date-y2k-1.
call "convert-year" using expiration-date, ws-date-y2k-2.
if ws-date-y2k-1 > ws-date-y2k-2
move xyz to abc.

A copy book will be inserted in each program where this is used.
We have macro's for TSO that make coding the call statements and changing
the IF statements very easy.

As far as I can tell only IF statements with > or < won't work. EQUAL's
should still work. COMPUTE's need special care but coudl be handled in a
similar way.

Any thought's on it?

BOB BROWN MBGF...@prodigy.com

The next Y2K on Usenet is in misc.jobs.misc on 4th October 1995:

I've been looking since '75.
In a recent discussion on the Y2K mailing list, we all agreed
There are NO OBJECTIVE STANDARDS.

This "Y2K mailing list" is most likely the one that David Eddy had first posted Y2K to in June 1995.

Y2K is used half a dozen more times on Usenet in December 1995 (including one referring to the De Jager list: "... where everyone else is discussing Y2K issues, including IBM's VM/VSE/MVS developers"), then it really takes off in 1996.

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