Just like Joel said: A good inventory editor will let you make new ones. But, to answer your question: Mob Spawners are nearly indestructable, so you can't pick them up.
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My life is all about punching trees, mining, crafting, building, punching spiders, fighting zombies, running from creepers, respawning, finding back my shelter and punching more trees. Yup, I wish I actually had a life.
Just so you know, you can also "disable" the mob spawner by placing 2 torches around it (Though, with the new update, I'd go for 4 torches to be safe). That way, the mob spawner stays preserved and you can build a mob trap around it when you want.
I'm not saying this is what you should do. Like I said, it's just so you know (if you didn't know already).
Oblivion is bliss to the wise.
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