I would like to add Backendless http://backendless.com to the list. It's pretty similar to Parse in terms of API and Dashboard. I've never used it but met the CEO and loved his vision for the future of the company.
Wow, this is an impressive list. Appcelerator looks good, but very pricey though. Why would you choose it over the others? The free version is the Titanium which is basically a Javascript SDK for native apps.
Sorry forgot to answer about why we chose appcelerator, I think its really about the amount of built in features. It allows you to get the ball rolling quicker, plus if you want custom it also has node.js custom server code capability.
For those looking at alternative BaaS services, we hope you'll take the time to evaluate StackMob. We've been working hard the last 24 hours to put together an easy path to migrate your apps from Parse to StackMob.
I always thought that Firebase and Backlift (Both are YC backed as well by the way) are doing something very similar, never had the chance to analyze the differences seriously though.
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")
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