I'm pretty sure I know what that little black line up the back of the shrimp is -- Sandy, avert your eyes now if you don't want to know ....
it's the shrimp's intestine, or digestive tract, or whatever they call the thing that gathers shrimp-poop.
So, you probably really do want to remove that vein. I've heard that you can get by without deveining if you're dealing with very small shrimp.
They do sell a special deveining tool. I usually use the tine of a dessert fork -- I just sorta "score" along the vein and then use the end of the tine to lift the icky black thing out. (But I'm sure if I keep reading this thread, someone will post something about the world's best shrimp deveiner, or the type of deveiner Alton Brown uses, or how they just can't live without their PC shrimp deveiner, and before I know it, I'll be scouring kitchen stores in search of one. )
Anyway, it is a little time consuming, but with seafood, I think it's better to err on the side of caution. I often spend the extra money to get them peeled and deveined at the store.
"We reject as false the choice between our safety and our ideals. Our founding fathers, faced with perils we can scarcely imagine, drafted a charter to assure the rule of law and the rights of man, a charter expanded by the blood of generations. Those ideals still light the world, and we will not give them up for expedience's sake."
--President Barack Obama, 1/20/09