The voltage and current rating of a motor, relay, solenoid, etc. is based on a variety of factors:
- wire gauge used for each winding
- insulation on windings and connectors
- materials used in construction
- allowed temperature increase (which is related to chosen materials)
- duty cycle (energize-time versus off-time)
- expected lifetime and abuse (used in an office appliance? a commercial kitchen? an industrial machine?)
For example, if you're dealing with a small motor salvaged from an office printer, it may only operate "once in a while" and the printer manufacturer chose a motor with relatively low duty cycle. This could imply that it can be driven with some voltage and current for a short time, but wouldn't survive lengthy or continuous application. The motor manufacturer might have built it to specification, which might mean a relatively small wire gauge, less cooling/heatsinking, and so on — to meet some price point.
An inexpensive fan motor might be designed for continuous operation, but has little torque and no cooling method (the designer knew the attached fan will provide airflow).
I have lots of salvaged motors and I use them from time to time in unimportant hobby projects. My method is to slowly increase voltage on a motor and measure the current and temperature. Not precisely, mind you, but in general to assess whether I think the motor housing is getting too hot, or if the motor sounds abnormal. There's nothing very scientific about the approach, it's just experience and best-guesses. As long as you aren't using the motors in anything important, where failure is no big deal, you should be able to obtain some good results and experience. But keep a fire extinguisher near!