App42 http://api.shephertz.com/
Kumulos http://www.kumulos.com/
Kinvey http://www.kinvey.com/
Apstrata http://www.apstrata.com/
Buddy http://buddy.com/
Stackmob https://www.stackmob.com/
Proxomo http://www.proxomo.com/
Iknode http://iknode.com/
Kii http://www.kii.com/en/technology
CloudMine https://cloudmine.me/
Applicasa http://www.applicasa.com/
MobDB https://www.mobdb.net/
Windows Azure Mobile http://www.windowsazure.com/en-us/develop/mobile/
FeedHenry http://www.feedhenry.com/
-- My favorite ones are in the order of preference following :
Appcelerator (currently using it )
App42 ( tried it )
Stackmob (tried it )
Kumulos
I have probably tried everyone one of those on the list, and a lot of it really depends which SDK some of those services offer.
Edit: a "Firebase vs Parse" question on Quora [0] (it's the first answer, no login required) made me realize that Parse is much more "mobile first" (tm), with a "full service" for mobile apps, whereas Firebase is taking "just" a subset (a very big subset) of data persistence, authentication and data security (e.g. server-less apps, which can be used in also in Mobile apps, but things like push notifications etc are more "role your own")
[0] http://www.quora.com/Firebase/How-does-Firebase-differ-from-...