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.
We are only using appcelerator cloud, our app is actually built in C# with http://xamarin.com
Appcelerator has free usage package
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.
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.
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