Gladiatorial Games
There are a ton of different options, depending on your sense of fairness and the blood thirstiness of your dwarves, but the basic premise is the same, build a stadium, with a cage connected to a lever in the stadium (or 2+ cages for pitting goblins vs. monsters you've captured).
Make sure the stadium can be made inaccessible.
Pull the lever(s) and let out the creatures.
Some options: Archery gallery
so your Marksdwarves can practice their aim.
Not very sporting .
Leave the Goblin some (or all) of it's equipment when you put it up against a fearsome foe.
Possibly sporting "trap" new Nobles, and make them survive a trial by combat before they're allowed to govern.
This might require a bit more effort (EG a bedroom w/ limitable access in both directions.
Danger Course.
Make a path lined with traps.
If you're feeling particularly generous, this could even lead outside of your fort.
For added variety, make the stadium floodable with Lava, Water or both.
gaming.stackexchange.com/users/1804/aslum
There is absolutely nothing wrong with keeping a Goblin and Kobold Zoo.
It's possible for dwarves to have a preference for goblins ("Urist likes Goblins for their Terrible Features"), and since Goblins (any non- friendly or tame unit, actually) don't need to be fed, they will (un)happily remain in cages indefinitely.
Just make sure to build a cage via the b uild menu, and voila!
Instant goblin petting zoo.
gaming.stackexchange.com/users/336/Raven Dreamer
If you do want to kill them, you can use i to make a p it over a cliff with spikes at the bottom and then use P to assign them to it.
Then your dwarves will take them and throw them off the cliff.
This won't work for goblin kidnappers and thieves(which
all kobolds are I think) though as they'll slip away from your dwarves and try to fight/escape.
You'll have to manually release them , and have your military dwarves kill them/flood the room(with magma!).
gaming.stackexchange.com/users/118/Ullallulloo
I always put them in a room where my archers can shoot at them but they can't get out.
Then I give my archers wooden arrows and just let them go at him.
Instant training pit.
gaming.stackexchange.com/users/9835/TrewTzu
I always create a room for caged creatures with hatch-covered holes in the floor leading into 3x3 fighting rooms below.
Each hatch is then marked as a pit using 'i' and creatures can be easily dropped into a room with a dwarf warrior-in-training waiting to try out some killing.
By keeping the cages near the pit designations, my dwarves don't have to move the cages far.
Note that there's nothing stopping you from making the fighting rooms several Z levels lower than the storage to make sure larger creatures have broken legs before the fight.
gaming.stackexchange.com/users/22621/mikebabcock
I've captured goblins with caged traps. I've already stolen all their stuff like explained  here , but now I don't know what to do with them.  Maybe my Dwarfs are happy seeing caged prisoners, but I'm not sure.  If I have to kill them, how do I do it?
Should I keep caged prisoners?
gaming.stackexchange.com
<dwarf-fortress>
gaming.stackexchange.com/questions/29419
gaming.stackexchange.com/users/12162/Ghislain Leveque
You can keep a Goblin zoo. You can also hold gladiatorial games, a danger course lined with traps or let your dwarves practise their aim. It is apparent that caging prisoners is allowed, although there are several ways to kill them.
Keeping prisoners is allowed. Prisoners could be killed using several methods such as Games or training exercise.