well, i believe that in the early days, google wanted to get into the mobile market as they saw an opportunity to provide choice and an alternative to apple's IOS. google did it the right way in forming a partnership with the major manufacturers to come up with an os that would be a cross platform os for all to use and to make it an open source os as well.due to this, it has allowed all manufacturers to mass produce android os phones.
i think the reason why it is so popular is that you can find an android phone at all price points. where as with an iphone you have to at least shell out $199 to get one on a two year contract.
also at the time the iphone was only available with att. i think that this was a mistake to have it only on att for the length of time that they were with them. they should have moved on to other carriers much earlier.
there were other os but i think they just were not as successful as android for various reasons. i think the one that came close to competing was the palm os. but i think that the phones themselves were the reason why they failed. and then there is backberry, but i think that they tried to adhere to a certain group of consumers(mainly business folks) and failed to try harder at broadening consumer interest.
i think overall it has much to do with advertising as the top manufacturers these days have done a great job at promoting their latest devices. samsung is a great example as their adverts and commercials are really good and does them a great job at creating hype for their phones like the s3 & note 2 and now s4.
as far as other os that has the google play store.....no. devices like the kindle fire have a modified version of android and does not adhere to ICS or JB. since all the apps in the play store are android, you will need an android device to use the apps from there.
i'm not even sure if i answered your question or not as it is a little vague....LOL
