Assuming the state and municipality don't prohibit such, house sparrows, starlings, rock dove (pigeon), and any other non-native species are generally fair game.
Important note: Make sure you can accurately and CONSISTENTLY properly identify european house sparrows. They look a lot like a number of other protected and valuable species.
Worse, their plumage changes throughout the year. Glass every bird carefully and never shoot a sparrow with a speckled breast (as it's either a song sparrow or a finch, likely).
Here's my favorite ID link:
http://www.sialis.org/otherbrownbirds.htmMark