API for Android or iOS connecting to EV3 by bluetooth There is official API for Windows, WindowsPhone8 and WinRT https://legoev3.codeplex.com/ it lets you connect to EV3 brick and control it remotely from your WindowsPhone.

Are there any libraries available for Android (Java) or iOS (Objective-C)?

I would like to write custom app for myself that will let me steer my own robots (using either Android or iOS device).
I have started a c++ iOS API at https://github.com/dsjove/legoev3cpp. Contributions are welcome.