Sustainable species of shrimp are shrimp that can be consumed without compromising the healthiness of their species or the integrity of the ecosystem in which they live. I like the position taken by the Monterey Bay Aquarium Seafood Watch with respect to shrimp and sustainability and recommend their guidelines as described below:
U.S. trap caught shrimp are your best choice since shrimp caught using this method have low-bycatch (unintended catch of other species of fish). U.S. organically farm-raised shrimp are your next best bet, followed by U.S. non-organically farmed and U.S. trawl caught shrimp. Choices that are not recommended include imported shrimp that have been non-organically farmed or trawl caught.
For more information about these recommendations and their relationship to sustainability, you can visit the Monterey Bay Aquarium Seafood Watch.