Running custom software on an Airport Extreme base station?
Currently there is no way to jailbreak either an Airport Extreme or a Time Capsule.

Whilst they are probably in the same order of difficulty as jailbreaking as say an iOS device, no one has really spent any effort on doing so.

Personally I think this is probably for the following reasons:


limited target audience (low numbers of product in the world)
limited 3rd party development support