Shrimp gone bad had a distinct odor, kind of like ammonia.That is, anything other than fresh, soft shrimp smell, with that hint of the sea. The fresh ones have a deeper grey color as well. Look for that deep color if they are wrapped, and if in doubt, notify the on-duty butcher that you want to open the package, and the two of you can determine it's good and fresh.
Frozen shrimp (you buy frozen) usually aren't bad, since they flash-freeze them right on the ship if done abroad and flown in, while local (like here in North Carolina) shrimp are driven in fresh from the coast, and hopefully sold that same day.
I am adding to the following, wise-ass answer, that was on the When you throw up after eating it. I hope that helps.