Crows and ravens are of the same genus although they are difference species, actually there are many different types of species of both crow and raven. The blackbird is not only a different genus, but also from a different family, although all these bird are of the passeriformes order. To clarify these terms all species are divided into seven classification levels, the blackbird is of the kingdom: animalia, the phylum: chordate, the class: aves, the order: passeriformes, the family: turdidae, the genus: turdus, and is the species T. merula. The raven and crow belong to the same kingdom, phylum, class, and order but are of the family: corvidae, and the genus: corvus. As I mentioned there are many species of raven and crow, all under the genus corvus. Here is a list of the North American crows and ravens: American Crow (C. brachyrhynchos), Chihuahuan Raven (C. cryptoleucus), Common Raven (C. corax), Fish Crow (C. ossifragus), Northwestern Crow (C. caurinus), Tamaulipas Crow (C. imparatus), and the Sinaloan Crow (C. sinaloae).
Basically the raven and the crow are related very closely, but the blackbird is a completely different bird.
In case you're wondering, cause I am, here is a human's full scientific classification: kingdom: animalia, phylum: chordata, class: mamalia, order: primates, family: hominidae, genus: Homo, species: H. sapien.
Hope that wasn't too technical for you, here are some pictures.
A Crow.
A Raven.
A Blackbird.
