In Wikipedia history there was a famous fork of es.wiki called Enciclopedia Libre Universal en Español, which split in some sense over policy disagreements. It remained larger than es.wiki for over two years following the fork.
Right now there are collaboratively-edited encyclopedias in some languages (at least Chinese) that are larger than Wikipedia, like Baidu Baike, which is much larger than zh.wiki.
There were at least two famous attempts to compete with English Wikipedia over policy disputes (Citizendium, which was concerned about verifiability and anonymity, and Conservapedia, which was concerned about the neutral point of view policy). These competitors haven't been very successful, but I can easily imagine people wanting to give each of them another go.
Right now there are about 100 online encyclopedias, each of which potentially competes in some degree with Wikipedia in some sense.
An example that's not particularly a result of an editorial policy dispute is Eric Weisstein's World of Mathematics, a super-great online math encyclopedia (that competes with Wikipedia for attention in its coverage of math). Another is the Stanford Encyclopedia of Philosophy, a super-great online philosophy encyclopedia. Both of these encyclopedias are stronger in at least some parts of their respective areas than Wikipedia is, and perhaps better even on Wikipedia's own terms (e.g., I bet the Stanford Encyclopedia of Philosophy manages to have a more "neutral point of view" on several philosophy controversies than Wikipedia currently does). But zero-rating probably means that people interested in these topics on some mobile carriers are more likely to look only at Wikipedia's articles, even if they're not the best online encyclopedia articles in those areas.
Edit: Eric Weisstein's World of Mathematics has been renamed to "Wolfram MathWorld". Although Wikipedia's coverage of most math topics is really excellent, I still think MathWorld has areas where it's likely to be even better.
Edit 2: Suppose you're interested in a particular religion's official take on some religious issue. Then an encyclopedia edited by adherents of that religious tradition (like one of https://en.wikipedia.org/wiki/List_of_online_encyclopedias#R...) may be more helpful to you than Wikipedia, for example because it may go into more theological or ritual detail, as well as more detail about polemics or apologetics from a particular religious view. That might actually be what you were looking for, but currently none of those religious encyclopedias is zero-rated by a mobile carrier.
Great point, but Baidu is super-rich, so it's unlikely zero-rating Wikipedia would make any effect on them. Not to mention zero-rating in Iraq probably not exactly relevant for zh.wiki :)
> Right now there are about 100 online encyclopedias, each of which potentially competes in some degree with Wikipedia in some sense.
In "some" sense, surely. To be really on the level comparable to Wikipedia by breadth of coverage and participation? Unlikely. None of them would be noticeably impeded by zero-rating Wikipedia in Iraq - most of them probably get next to zero participating from Iraq anyway. Same probably applies to any other place where Wikipedia Zero works.
> but currently none of those religious encyclopedias is zero-rated by a mobile carrier.
Because it doesn't make sense to zero-rate niche sites. By the same vein I could say Wikipedia competes with a knitting site run by my friend because if you want to know about knitting, I'd go to a knitting site, and it's not zero rated. That doesn't make much sense to me - if you want to enable minimal service to people, you choose something with broadest coverage, not with deepest one, because deepest one would necessarily be niche.
Even Mathworld/Weisstein's World of Mathematics isn't always right either.
I found an error once, and sent it in (it was something to do with graph theory, and the equation was missing a +1 or something, which was sort of critical). I checked about a month later and it hadn't been fixed, I can't remember what it was now, I really wish I could. It was something to do with "n/2 + 1" and they had written "n/2".