Larísa has an interesting post up on the subject of "WoW is dying", where she concludes (correctly I think), that it is more a case of people thinking "I'm personally bored of WoW, and that means WoW must be dying" than anything to do with the actual state of the game. She links to a very interesting post by Gronthe on Blizzard's financials, which shows that the net revenue of Activision Blizzard is on a constant upward trend. And anyone who believes that Blizzard isn't going to make a profit with Cataclysm, Starcraft II, Diablo III, and their next MMO, needs to get his head checked.
But while the chance that Blizzard is going broke and having to shut down the World of Warcraft servers anytime soon is infinitesimally small, the subjective feeling of "WoW is dying" some people have is based on other, more personal, experiences. For example I am pretty certain that player activity this summer is going to be relatively subdued. That doesn't necessarily mean a lot of people unsubscribing, as a lot of people might just let their subscription keep running and just play less. But it does lead to less activity on the servers, more difficult time to get raids together, and associated guild drama with potential for some guilds folding due to being unable to raid.
The other major factor is burnout. The average player is playing World of Warcraft a thousand hours per year, and with WoW in its sixth year that adds up to a lot of hours. The truly astonishing thing is that people can play a game for several thousand hours, not that they are burned out at the end of that. We know that WoW is in the top 10 of PC games sales charts nearly every month, so as the game doesn't appear to be growing any more (no new servers, no press releases on new player number records), nor shows significant signs of shrinking (no server mergers), we must assume that there are about as many people leaving World of Warcraft every month as there are new game sales. Again, over the years that makes a lot of ex-WoW players.
So while "WoW is dying" certainly isn't true in any absolute sense of the term (unless you take John Maynard Keynes view that in the long run we are all dead), it is perfectly possible that *your* personal World of Warcraft is dying. Your guild imploded, your best friends left, you are stuck in pickup groups with clueless n00bs, and you are burned out and bored, until you quit and WoW is dead *for you*.
But objectively speaking World of Warcraft has quite a good survival strategy. Given that eventual burnout, especially of those who play a lot, is inevitable, designing the game with new players and casual players in mind is probably the best possible way. Of course that leaves the veterans furious: As they learned a lot about WoW in the past years, and optimized the performance of their characters, they would need the challenge level of WoW to constantly go up for the game to remain interesting. Instead the developers make many aspects of the game more accessible to new and casual players, and remove unnecessary complexity. Also the amount of content an expansion plus all patches adds to World of Warcraft is more suited to a leisurly pace of consumption than to hardcore playing. The more you play, the faster you just run out of things to do. From a business point of view that makes total sense, because a new and casual player pays as much money as a hardcore player. But of course for the hardcore players that can be frustrating, and as it is more often them who populate blogs and game forums, they vent their frustration in doomsaying. In reality World of Warcraft isn't dying, it is just moving away from the needs of that player group.
The financial brilliance behind that development strategy becomes apparent whenever the next expansion is released. If a large part of the ex-WoW players are people who got bored and burned out, an expansion promising new content and new challenges is likely to bring them back, at least for a while. Thus they spend money on the expansion box, plus some months of subscription, and Blizzard is making tons of money. It is pretty much certain that Cataclysm will again break all possible records for first-week sales, and that the subscription numbers will peak again. So is World of Warcraft dying? Not unless it suffocates under a pile of money.