Should I keep caged prisoners?

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.

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 build menu, and voila! Instant goblin petting zoo.

If you do want to kill them, you can use i to make a pit 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!).