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I came accross the is question What are the consequences to breaking the ISS? and wander how would a spacecraft be made to stop spinning from the outside?
Scenarios might include (but are not limited to) things like recovery, repair, or refueling of an out-of-control, malfunctioning, or out-of-fuel satellite.
So long as the object you wish to slow is made of metal you can slow it by putting a ring of magnets around it. How fast this will work depends on the metals involved. I do not believe this can bring it to an actual stop, however--the slower it turns the less braking force. Edit: Yes, you can stop it--if your ring is spinning the velocity won't go to zero. Three notes:
1) Remember Newton. The ring is going to spin up as your target spins down. You'll need rockets to counter this.
2) At least some of the energy involved appears as heat in the metal. If you have a large, rapidly spinning mass with only a small metal component you could end up with a lot of heat.
3) This is quite sensitive to the distance. If you can't get the magnet band right up next to the metal (either a non-metallic outside, or projections that you need to clear) it's going to be all but worthless.
(Note that you'll see this same system used in various systems here on Earth as it provides basically foolproof braking of something that is moving on a track of some kind. I have specifically heard of it in roller coasters.)
BTW: Issac Asimov, The Martian Way, used this to capture the fuel tanks.
An alternative would be to enclose the object in an air tight container and pump some air inside. Drag would slow down the craft.
The main issues for the aerodynamic drag technique will still be the same as for the magnetic drag technique:
