If you crafted the gem in, it cannot be removed. There is a possibility you can salvage the effect out in a component though. --- WARNING: I am a mediocre gamer. Don't take what I say too seriously. PSN: njp1589
If you socketed a gem in using sagecrafting, you can remove it with maxed out sagecrafting skill.
If you used a gem using blacksmithing, you can't separate the gem out, but you may be able to get a component that has the gem's attribute by salvaging. --- Phosphorus? Pfffft, who needs 'em?? http://img585.imageshack.us/img585/5206/takeyourtime.jpg
Any gems that you put into slots can be removed by certain NPCs. Most of the times they'll be ones standing near a sagecraft altar. --- Playing Borderlands GOTY: Lilith-69-PT2.5, Roland-36-PT2, Mordecai-11, Brick-7.