WoW has a long history of removing content with the release of new expansions. While the most obvious case of this was the removal of, for example, Zul Gurub, and with it, the old Tiger and Raptor mounts with the release of Cataclysm, there have been several other examples of now classic titles or items that are no longer obtainable because the quests required to reach them, or the dungeons in which they dropped, or whatever, have since been removed from the game.
And just as the removal of content is something of an age old tradition, so is using the lull before a new expansion to farm up those last few achievements, to waste time grinding that one rep that's about to be removed, or farming a dungeon to get that one last piece of that old tier .5 gear that you won't be able to get anymore to complete your set.
But so far, as the release date for Mists rapidly approaches, I'm yet to see a list of exactly what's going away, which is of course, an important tool before engaging in such an exercise.
So, what's being removed? I'm especially interested in titles, achievements, mounts and pets, but any notable reputations, set items or cosmetic items, are of course worth mentioning as well.
Best Answer
One thing that has been confirmed by Blizzard as changing is the drop rate of some raid mounts will decrease on release of Mists of Pandaria, specifically Smoldering Egg of Millagazor and Life-Binder's Handmaiden, both currently 100% drops on heroic raid encounters.
As far as we know at this point there are no dungeons being removed, no old questlines being removed and no old reputations being removed. Almost all new content, with the exception of Pet Battles, the Fall of Theramore and Heroic SM and Scholomance, is Pandaria-based. As far as we know, achievements, titles, mounts, etc, will remain achieveable with the usual exception of the rotating PvP mounts.
Doing a comparison of data-mined Feats of Strength backs this up, with only new Realm Firsts, new expansion Feats and the PvP stuff the difference between the current list of Feats and the list for Mists.