European Starlings are the first example that come to mind. Some geniuses decided it would be a great idea to introduce all of the birds mentioned in Shakespeare's plays, so in 1890 they released Starlings into Central Park. There were prior attempts to introduce them, but this seems to be the one most cited as successful. European house sparrows were similarly introduced, although that may have been an attempt at biological pest control rather than someone's fancy.
It seems not long after that is when congress started to take some notice that maybe bringing in new species willy nilly wasn't a good thing, as bans against introducing new species were part of the Lacey Act of 1900. I don't know what species in particular spurred this inclusion, and I haven't as yet been able to find a mention of when Starlings or house sparrows first became recognized as detrimental to the native bird population. Their exclusion from the protections of the Migratory Bird Treaty Act of 1918 is the only control measure that the federal government has been involved in to my knowledge, I can't say for state and local governments. As many countries have found eradicating an introduced species without harming the natives is darn near impossible in many cases, and judging by the number currently gobbling up my suet Starlings and sparrows are here to stay.