The European Blackbird is a thrush (Turdidae, snicker if you must), and not closely related to the blackbirds found in the Americas, which belong to the Icteridae, which includes the New World orioles, meadowlarks, grackles, blackbirds, and various tropical groups. The European Starling is in yet another family, Sturnidae, and the crows and ravens are in the family Corvidae.
There are a bunch of “blackbirds” among the Icteridae:
Rusty Blackbird
Brewer’s Blackbird
Red-winged Blackbird
Tricolored Blackbird
Yellow-headed Blackbird
The grackles are also in the Icteridae and usually considered to be “blackbirds” in the broad sense:
Common Grackle
Boat-tailed Grackle
Great-tailed Grackle
So are the cowbirds:
Brown-headed Cowbird
Bronzed Cowbird