It's easier to take note of the circuit they come from, than to reverse-engineer the part (and potentially have to take it apart and count turns!).
A standard ATX power supply uses a half-bridge inverter stage, supplied by 320VDC, switched at 50-100kHz with a TL494. This puts useful limits on how many turns, amps and how much flux the transformer handles on the primary, and what the output turns are (for 5V and 12V).
Likewise, flyback supplies (typically the standby/aux supply in an ATX, or most power supplies under 100W) may have a 90-250VAC input, or a more limited range, in either case being around 300V or less on the primary side, probably at frequencies of 50-130kHz or up to 400kHz. Typical circuits for the controller chip (e.g., UC3842, TOPSwitch/FPS/etc.) are almost always recognizable.
There isn't much point using a transformer outside its intended range; you can scale frequency and voltage proportionally (half frequency == half voltage), and for flyback applications, you have some freedom over how high the flyback goes (say +/- 50% from intended application).
Of course, you can always use a transformer backwards, providing your circuit is also backwards. (Example: an ATX supply has a FWCT rectifier and choke-input filter. You'd use a 12V supply, series choke, and push-pull transistors to drive the "secondary" (which is now your primary), and instead of a half bridge on the HV side, a full-wave doubler to rectify it.)
Reusing small flyback transformers is a good way to get modest voltages (say 100-500V at ~mA) from battery or low voltage sources.
Tim