Crows are black omnivorous birds sometimes associated with battles due to their taste for carrion.
The crows encountered by Bilbo Baggins and the Dwarves during the quest to Erebor in T.A. 2941 were mostly harmless. During the scouting expedition to the Front Gate of the Lonely Mountain the crows were considered "ominous" and Balin distrusted them, though later he called them merely "nasty suspicious-looking creatures at that, and rude as well".
The most feared variety in the Westlands of Middle-earth was the large type known as crebain. On 8 January 3019 the Fellowship entered Hollin and were spied upon by these large crows from Fangorn and Dunland. The Rohirrim were aware that Saruman made use of crebain; on 30 February Éomer told Aragorn that Saruman's "birds of ill omen are abroad in the sky". Crows may actually just be another name for Ravens as they looked and acted exactly the same.
A Quenya word for "crow" is quáko, derived from Primitive Quendian k(a)wāk. Another Quenya word for "crow" is korko, and the Noldorin cognate of the same meaning is corch. In Gnomish, one of Tolkien's very early conceptions of an Elven language, the word for "crow" is crunc (pl. crunghin).
Adûnaic also had its own terms for a crow, specifically khô in "common" gender singular ("crow", as a species/creature), the plural khôi ("crows"), and the dual (pair-plural) khôwat ("a pair of crows"). Tolkien's notes on Adûnaic vocabulary and grammar also indicate that the more archaic forms of the term were likely khaw, later khâw, eventually evolving into khâu (with the Adûnaic diphtong âu), while the plural of these older forms would apparently be khâwî(m). However, both khâu and khâwî(m) would likely be declensions in the subjective case of the noun, rather than in the nominative case. The objective case of the noun would be khôwu.   
Other versions of the legendarium
In J.R.R. Tolkien's plot notes for the second phase of writing The Hobbit, there was no distinction between crows and ravens as ominous birds. When the scouting party went to view the Front Gate Balin did not like the ravens nearby, stating that they looked "like spies of evil". However, when the Company needed to learn of the death of Smaug Tolkien "rehabilitated" the ravens, making them friendly to the Dwarves, and replaced all negative raven-references with crows.
- J.R.R. Tolkien, The Lord of the Rings, Appendix B, "The Third Age"
- J.R.R. Tolkien, The Hobbit, "On the Doorstep"
- J.R.R. Tolkien, The Hobbit, "The Gathering of the Clouds"
- J.R.R. Tolkien, The Lord of the Rings, Appendix B, "The Great Years"
- J.R.R. Tolkien, The Lord of the Rings, The Fellowship of the Ring, "The Ring Goes South"
- J.R.R. Tolkien, The Lord of the Rings, The Two Towers, "The Riders of Rohan"
- J.R.R. Tolkien, Christopher Tolkien (ed.), The War of the Jewels, "Part Four. Quendi and Eldar: Appendix D. *Kwen, Quenya, and the Elvish (especially Ñoldorin) words for 'Language'", p. 395
- J.R.R. Tolkien, Christopher Tolkien (ed.), The Lost Road and Other Writings, Part Three: "The Etymologies", p. 362 (root KARKA-)
- J.R.R. Tolkien, "I-Lam na-Ngoldathon: The Grammar and Lexicon of the Gnomish Tongue", in Parma Eldalamberon XI (edited by Christopher Gilson, Arden R. Smith, and Patrick H. Wynne), p. 27
- J.R.R. Tolkien, Christopher Tolkien (ed.), Sauron Defeated, "Part Three: The Drowning of Anadûnê, with the Third Version of The Fall of Númenor, and Lowdham's Report on the Adunaic Language", p. 426
- Adûnaic - The Vernacular of Númenór, "Adûnaic Wordlist", Ardalambion (folk.uib.no) by Helge Fauskanger
- Adûnaic - "khô", "Adûnaic Words", Eldamo.org by Paul Strack
- J.R.R. Tolkien, John D. Rateliff (ed.), The History of The Hobbit, Mr. Baggins, The Second Phase, "Plot Notes B", p. 362
- J.R.R. Tolkien, John D. Rateliff (ed.), The History of The Hobbit, Return to Bag-End, The Second Phase, "The Lonely Mountain", p. 472
- J.R.R. Tolkien, John D. Rateliff (ed.), The History of The Hobbit, Return to Bag-End, The Second Phase, "The Lonely Mountain", note 4, p. 479