Sure.
House sparrows (Passer domesticus), starlings (Sturnus vulgaris), and pigeons (Columba livia) were introduced from Europe and have become much more numerous than the native species. In some instances they out-compete the natives, although to my mind clearing the forest first for agriculture & then for cities also had an impact.
Small native birds include kinglets, hummingbirds, warblers, sparrows, finches, tanagers, flycatchers, swallows, chickadees, nuthatches, and others I haven't listed--much of the population in bird guides, in fact.
(Other introduced species are the pheasant (Phaseanus colchicus) and the mute swan (Cygnus olor) commonly found in parks. I think those are the main Eurasian birds that have established themselves in eastern North America, although there is the occasional escape/blown-off-course migrant/barnyard duck-mallard cross.)
Does that answer your question?