"Your circuit is bad, and you should feel bad"?
Oscillation is either a topological problem (e.g., you put feedback to +in when you meant -in), or a feedback problem (too much junk in the feedback loop and it's phase shifted to hell). Either way, you have to start with the circuit.
There isn't anything general that can really be said, aside from recitations of Nyquist stability criterion. As for what's violating the criterion... you'd have to look.
Don't forget to inspect everything related. Supply pins don't have infinite PSRR at just any frequency. They are inputs, just not very good ones! They are also quite good outputs, since any current drawn from the output pin is also drawn from +V or -V. For both these reasons, bypass caps are a good idea.
Don't ignore the reference voltage. Usually this is GND. Sometimes it's a floating level between -V and +V. Sometimes it's explicit in the circuit. Whatever it is, it needs good bypass too, otherwise all the impedances driving it give a place for AC signals to roam, and you get feedback loops between stages.
Tim