Are the older servers being shut down? Is Warcraft Forever replacing World of Warcraft?
No and no.
So, Warcraft Classic spun off as its own thing about four years as a parallel track to the retail version of the game.
Classic has since had servers that were vanilla only, vanilla+TBC, vanilla+TBC+WotLK, vanilla+TBC+WotLK+Cataclysm, vanilla+TBC+WotLK+Cataclysm+Pandaria and, probably most importantly, a Classic+ vanilla version called Season of Discovery in which they added new content, tweaked old stuff and tried new things.
All of which is accessible with the same World of Warcraft subscription that gives access to retail. (In practice, most people either play retail or play classic, and talk crap about the players on the other side, although both sides of the aisle are very robust and would probably be the second-most popular MMO out there all on their own).
WoW Forever is going to be a new ongoing Classic+ set up with no end date (Season of Discovery, as its name implies, was a limited time server and stopped receiving content updates and might have shut down), and flesh out the World of Warcraft setting with an alternate take on WoW's first year (meaning not all vanilla raids will be available immediately, for instance, and when they do appear, they will likely be tweaked, which is good, because some of them were pretty basic -- Molten Core is basically just a bunch of caves full of monsters standing around waiting to die).
Retail isn't going anywhere. Midnight, the current expansion, is halfway through and has been pretty great, and is leading into The Last Titan, which will wrap up a lot of story lines that go back as far as Uldum in vanilla. And it's not the final expansion -- something people have been talking about since WotLK -- since they've laid track for the future with new enemies like the racist Arathi Empire and their unknown continent and journal entries from NPC mariners about new continents hidden away by magic.
WoW Forever is basically an alternate take on retail, in that it'll be ongoing content that they're saying will have a level 60 level cap indefinitely with alternate ways for characters to improve (like an achievement-like Legacy system that improve all of your Forever characters on your account* with things like how fast they accumulate rest) and be set on the Eastern Kingdoms and Kalimdor only, although with blank spots in the map filled in (there's a new zone north of Redridge, for instance) and a flying island with a neutral PC race of Skyborne elves (the really,
really high elves).
Both versions of WoW are pretty darn compelling. I've got a character I've been playing in retail since day one of WoW back in 2004, but if I didn't, Forever would be extremely tempting.
* Retail has its own version of this, called "
warbands," a term which Forever very noticeably avoided using. I suspect there are a lot of lessons that retail and classic have learned from each other's development, but to keep people from freaking out about the line between them being blurred, they'll use different names for what are realistically the same thing.