I'm no transformer expert, but here's my take:
Lots of stuff have transformers in them - identifying the parameters will usually be impossible. The parts numbers are house parts and impossible to trace. Even if you know the turns ratio, you don't know the wire gauge, impedance, current rating, or core type. Many have multiple taps.
Power supply transformers aren't so bad - hook up the primary to line voltage and measure the secondary AC voltages. You still have to guess about current and power capabilities.
Even if you're able to find the data, how're you going to know how to use it in a circuit, unless it just happens to be one that is called for (a likelihood comparable to winning the Power Ball Lottery.) I suppose if you get it out of a high end audio preamp or other audio circuit it might be useful, but except for power supplies, I doubt you'll find anything in consumer audio stuff.