Honestly, unless Blizzard makes an MMORPG out of StarCraft or Diablo, or unless maybe BioWare makes one out of the Mass Effect universe, or unless Bethesda makes one out of Fallout... I can't see any MMORPGs that I would qualify as the "next big one" (I.E. big enough to actually compete successfully against World of WarCraft, which I don't think would ever be possible anytime soon, and perhaps never until WoW 2 comes out).
But as far as "others" go (not big, just the next ones on the horizon)...
There's the NA version of Blade & Soul in beta (every week end, or something along the lines), it will probably come out early next year (" Q1 2016 "). It's not a "big" MMO per se, and it's about two years late for a NA release (in my opinion, it should have competed against TERA when that one was still fresh-enough here). But it does look somewhat interesting (the combat mostly, it's dynamic, no tab-targetting), although I have my doubts as to how long it'll stay active.
What I would call certainly a notable MMO (and might become big over time) will be EverQuest Next, whenever it's completed, maybe in a decade from now (not sure if that's actually that much of an exaggeration, considering how ambitious they are with it). They've been working on it for what... 4 or 5 years by now (I mean they started before announcing it obviously, the announcement itself is more recent). Whenever it does come out I suppose it'll be one to keep an eye on.
And there's Black Desert, which supposedly hasn't been doing well in Korean recently. Time will tell how it 'survives' here. It does look very good, however, there's also the possibility to build your own house, and considering how complex the character creator is I can definitely see tons of devoted role-players being active on a regular basis. I would go as far as saying that they'd just ignore most of the game's content and just log-in for role-playing with others. But anyway, RP'ing or not, Desert Combat's dynamic combat system seems fun, but from the multiple videos I've seen (of the Korean version mostly) the PvE segment looks like a borefest.
That's about what I can think of right now (there's MANY more, especially in the F2P field but I won't bother listing them all, the F2P section on Steam is more than enough for that purpose).