A capacitive load (ie. driving a cable) can destabilize an op-amp circuit as well. A unity-gain stable op-amp may not be stable if driving thirty metres of cable. Basically, this increases that delay that John was talking about - by adding capacitance on the output. The 'hack' is to place a small resistance between the op-amp and the cable (often between 20 and 100 ohms), and sometimes a small capacitor is placed directly from the OUT to the IN- on the op-amp chip, usually somewhere between 5 and 33 pF. This trick can often stabilize an op-amp even without any other changes.
Some audio op-amps don't do well without a capacitor between V+ and V- (the power supply rails) right by the chip, and others (like the TL072) are very tolerant of supply decoupling. Some circuit designs have issues (and often these are design mistakes) that don't show up with one op-amp, but if you put in a 'better' - or even 'different' op-amp in its place, it oscillates as well. Sometimes 'different' means 'same part, different manufacturer'.
A good example of marginal design is the Soundcraft 2400, which has some oscillation issues. After struggling with a few cranky compressors (that would cause the board to do funny things), I narrowed it down and found the 'fix' was to add a 10pF across a couple of the op-amps on the channel strip. Interestingly enough, these were correct on the monitor/group strips and master section, but were incorrect on the channel strips.
-Dale