A common hassle linked to having a phone is spam [robo]calls.
I'd love to have an IVR app answering my phone calls, so that it plays a pre-recorded menu and asks callers to press a digit to actually call me. Ideally, I would ask people to press a different number depending on the call's nature (think commercial offer vs job-related call vs friends/family vs emergency), and I'd love to even have a "secret" code for special people that would make the phone actually ring even while I'm asleep.
Android being open-source, I guess the Telephone app source should be available, so maybe someone already built some programmable capabilities on top of it?