It seems like it would be super useful if an app existed for iPhone/Android that emulated a Bluetooth keyboard or mouse. e.g., you turn on the app, and suddenly you can type on
The public iOS APIs do not currently appear to expose any functionality that would allow an app to make the iOS device to appear as a generic keyboard HID on Bluetooth.
However, iOS apps (iOS 4.2 and later?) can use external Bluetooth keyboards for input.
I'm surprised nobody has answered pointing out BlueputDroid as an Android solution for that. At the link you can find further information about device compatibilities.
I know this thread is rather old but I think it's worth to let it documented so others would end up here as me and will find an answer, at least for the Android half of the question.
EDIT: if you have problems to get your device connected to your ps3 like I did, try this out: http://forum.xda-developers.com/showthread.php?p=19881739#post19881739
This is possible on Blackberry 10 devices. Use the app called: bluetooth keyboard-mouse. I have been looking but I don't think Android or IOS have capability to appear as a bluetooth hid device