Is it possible to develope android games at android devices?

To a limited extent, yes.

There are several Android compilers that run on Android. I have seen AIDE discussed in positive terms, although it isn't the only one out there.

A few moments on the app store pulls up what looks like seven or so free and paid IDE-style development environments and compilers. Most are aimed at the Asus Transformer (which has an attachable keyboard) or devices that let you attach a keyboard through USB or other means.

Debugging a full-screen game on the device will be much more difficult than using a remotely attached debugger, but I imagine it is possible.

I'm not sure... I've tried AIDE a long time ago and it was alright to make tweeks until they removed almost all the functionality from the free version.

You really need a decent computer to do any android programming mainly because eclipse is so heavy.

Also I'm not sure how you would install any of the common third party libraries used in android development on your phone let alone upload it the play.

Not to mention that having the smart phone keyboard as your primary input device would make for very slow typing.

So it is possible but hard and limited. Thank you for the answers.