I have several servo and ordinary DC motors. They would all have gearboxes.
I want to put them through their paces but without damaging them. I know that stall current is the maximum they'll take. But would taking them all the way up to the stall current damage them?
How can I know where to stop in terms of the force applied to them? Please elaborate on both servo and DC motors.
When you say "put them through their paces" are you intending to build some sort of mechanical test rig, with a way to apply a force, or even a brake to them?
Have you got the datasheets for the motors and servo's so you can, at least, get some estimate of what their stall current is?
If you hold a small DC motor stalled for an appreciable time (more than a few seconds), then it may be permanently damaged by the heat (depends to some extent on the motor, sorry to be vague). With either a motion encoder, or current monitor, you should be able to detect a single motor being stalled. As you probably know, model servo's are usually DC motors.
I saw a delightful test rig a couple of weeks ago.
A guy had three identical motors meshed around a common gear.
1 - the motor under test
2 - a motor used as generator, so he could measure the amount of energy, and detect a stall
3 - the motor generating the force against motor 1.
So he could monitor whether the motor (1) was moving, and by how much, by measuring the output of the generator (2), and apply a braking force with a motor (3).
He could control the whole thing from a single microcontroller with two sets of H-Bridges.
You could build a similar mechanism.
Put a small (low thermal inertia) temperature sensor on the motors too, as a backup measure. Thinking about it, this might be useful anyway to characterise the motors (depending on what the end goal is).
You could also make a pretty good motion encoder for about a $1 with a Hall effect sensor and a magnet. That would give a good way to measure speed, and detect a stall.
HTH
GB
In other words, if motor is supplied with stall current for more than few seconds, it will get damaged by heat. So, one just needs to monitor the current going into the motor and it gets as high as 90% of stall, immediately disengage.
How can one use Hall effect sensor to measure movement. You thnik attach the magnet to the shaft and than measure Hall effect current/voltage?
What percentage of the stall current is optimum for continuous running of the motor?
In other words, if motor is supplied with stall current for more than few seconds, it will get damaged by heat. So, one just needs to monitor the current going into the motor and it gets as high as 90% of stall, immediately disengage.
Yes, that would do, except the 90% would need some calibration.
The datasheet might be a bit conservative and overstate the stall current, so you might miss the failure point until it releases smoke 
How can one use Hall effect sensor to measure movement. You thnik attach the magnet to the shaft and than measure Hall effect current/voltage?
Yes, that's the idea. The Hall sensor will give a nice sine wave as the magnet spins past it. If you're only spinning at, say, 20,000rpm or less, then you could read it with an analogue input. If you want much faster, get a Hall switch IC, and read the digital input.
What percentage of the stall current is optimum for continuous running of the motor?
I believe it depends on the motor.
Very well specified motors, with good datasheets, will give the torque vs current curve. When you look at it, you'll see a 'knee' where it quickly reaches stall.
[edit]There are some examples about 60% of the way down: LEGO 9V Technic Motors compared characteristics
Some motors are specified directly for efficiency like this: MFACOMODRILLS.COM
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AFAIK, its good to keep well away from that knee, so that reasonable variations in opposing force doesn't trigger the thing stall. It can be run closer to the knee if the variation in force is small, or there is a good way to protect it (i.e. good stall monitoring which will quickly switch it off).
Sorry to be vague, but "More Input" 