I've seen coming Soon™ attached to some Valve and Blizzard products, but did it start with one of them (and if so, which)? What was the first game (or other product) that was to be launched with the blatantly tongue-in-cheek Soon™?
I think the phrase itself is older than World of Warcraft; certainly older than the Burning Crusade expansion. I remember seeing the phrase on Bungie fan sites during the Marathon and Myth heyday. For example, here's a post from 2001 on myth.bungie.org where Soon(tm) appears, and here is a page on the Marathon's Story website that contains the phrase all the way back in 2000 (you'll have to search the page for "soon(tm)" as it's a big page). Both of these predate WoW's announcement in September of 2001.
I would venture to guess that the phrase has been around almost as long as release dates have been left unannounced for popular titles, which is a very, very long time and may even predate the web (which is to say, you may need to dig through AOL discussion board or Usenet archives to find the real origin).
Given that it's been around so long, I'd be surprise if Blizzard were the first to ever "officially" use the term as a way of saying "we aren't telling you the release date yet."
Soon™ almost certainly originated from the term "Real Soon Now" that was originally popularized by Jerry Pournelle to describe software with vague release dates in his articles in BYTE magazine. He used the term at least as early as 1984 (BYTE Magazine, November 1984, page 374, first column).
It became very popular on Usenet as well and there it combined with the then-popular trend of appending trademark or copyright (registered trademark) symbols to anything and everything. I've found a reference to such tongue-in-cheek use gaining momentum after AT&T released its UNIX System V as "AT&T UNIX®" in 1983 and they were reportedly quite anal about preserving the copyright symbol. I can't find any primary sources to confirm that story but the popularity of "(TM)" in Usenet is evident from the archives.
I managed to get the hidden date filter working in Google's Usenet archive and that turned up dozes of uses of the term "Real Soon Now (TM)", the earliest dating to 1989. The short form "Soon (TM)" was rarer but still turned up twice in 1990.
The oldest Usenet source I've found where the term was used by the owner of a product approaching release was in the message signature of Carl-Eric Menzel which described his website's being launched "Real Soon Now (TM)". That can be seen in the support query he sent to his hosting service Pair Networks in the form of a Usenet post from 1998. Since you're asking specifically about the first product to be launched with the term, I guess the (now defunct) bitforce.com website may qualify for that honour. However, given the apparent popularity of the term it's likely that other authors or owners used the term well before that. Who was first may be impossible to determine and depends on what you believe qualifies. To my knowledge no product was actually marketed with "Soon™" but there will be plenty of self-deprecating references by developers.
Actually, I used to use it in a game called EverQuest back in 1999. Before that, I used it on a BBS called "HOT BBS" as far back as 1982. I used to have a submenu on my BBS where I listed features that were coming. It was called "Coming Soon" for a while, but the jokes started that I never finished things on my Coming Soon list (I was a teen, and girls had started becoming interesting). So, as a self-deprecating joke, I changed it to the SOON(tm) page.
Years later, when I was a guide and eventual coder on EverQuest, I used to constantly respond to questions about bugfixes or features with the simple phrase "SOON(tm)". It caught on, particularly when some players started attaching SONY = SOON(tm) ONLY NOT YET.