I have gotta agree with MS here.
Without doubt, Apple own the most famous 'App Store'.
Others exist of course: handset manufacturers building ecosystems around their devices. Indeed, I recall some ecosystems trying to collaborate together to make their apps deployed on one ecosystem simple to deploy on others. 'Write once, run anywhere' mantra. (Can't find the link at the moment.)
The elephant in the room is Microsoft. They have Microsoft Marketplace which seems to have gone through an evolution or two, according to Wikipedia.
In 90s, surely this could have been the mother of all App Stores, as Microsoft could have leveraged its incredibly powerful developer network to promote developers' software to each other and the world.
Heck, the thing could have had virtual currency with:
- e-commerce store for all apps that ran on MS platforms
- developers purchasing software components from Microsoft and each other (Indeed it could be possible that MS could defer licence fees for developers purchasing its software until the software made money on the e-commerce store)
- reviews + forums
Perhaps this existed and I missed it or perhaps MS missed the elegance of the concept completely, but I bet Microsoft are kicking themselves for not building a really solid wall to nurture their developer community.