The band's influences include Van Morrison, R.E.M., Mike + The Mechanics, Nirvana, Bob Dylan, and The Band. They received a 2004 Academy Award nomination for the song "Accidentally in Love", which was included in the film Shrek 2.

According to the official band website, Counting Crows has sold over 20 million records worldwide.

Singer Adam Duritz (former member of the Bay Area band The Himalayans) and producer/guitarist David Bryson formed Counting Crows in San Francisco in 1991. In addition to his experience in The Himalayans, Duritz had contributed to recordings by the Bay Area group Sordid Humor ("Barbarossa"), though he was never a member.

Counting Crows began as an acoustic duo, playing gigs in and around Berkeley and San Francisco. Another friend, guitarist David Immerglück, played with them from time to time, though he was not an official member of the group, experimenting with other musicians in the area. As the emerging band recorded some demos, and later, as other musicians joined the duo to make a full band, Immerglück recorded with the others on some of the songs on their first album. He declined joining the band at the time, because of his membership in two other locally popular bands; Monks of Doom and Camper Van Beethoven. By 1993, the band had grown to a stable lineup of Duritz as vocalist, occasional pianist, and primary songwriter, Bryson on guitar, Matt Malley playing bass guitar, Charlie Gillingham on keyboards, and Steve Bowman, as drummer, and the band was a regular in the Bay Area scene. The same year, the band signed to Geffen Records. January 16, 1993, the band, still relatively unknown, filled in for Van Morrison at the Rock & Roll Hall of Fame ceremony, and was introduced by an enthusiastic Robbie Robertson. At the ceremony, they played a cover of Van Morrison's "Caravan".

Before signing to Geffen, the band recorded demo versions of a number of songs, known as the 'Flying Demos'. These later surfaced among the Counting Crows fanbase. Tracks include "Rain King", "Omaha", "Anna Begins", "Einstein on the Beach (For an Eggman)", "Shallow Days", "Love and Addiction", "Mr. Jones", "Round Here", "40 Years", "Margery Dreams of Horses", "Bulldog", "Lightning", and "We're Only Love".

Some songs from the tape later resurfaced (in reworked versions) on the band's debut album August and Everything After.

The band took its name from a divination rhyme about the crow, heard by Duritz in the film Signs of Life. The rhyme begins the third verse (around the 2:07 mark) of the song "A Murder of One" on the album August and Everything After : "Well I dreamt I saw you walking up a hillside in the snow / Casting shadows on the winter sky as you stood there, counting crows / One for sorrow, two for joy / Three for girls and four for boys / Five for silver, six for gold / Seven for a secret never to be told."

In the poem, the act of counting crows is particularly useless. This recalls a traditional rhyme: "One crow means sorrow, two crows mean joy, three crows a wedding, four crows a boy, five crows mean silver, six crows mean gold, seven crows a secret that's never been told." In the United Kingdom, the rhyme is well known but uses magpies rather than crows. A popular superstition is that if one sees a single magpie, one should greet it to deflect the "sorrow".

From the beginning, Counting Crows focused on live performances. The band's debut album August and Everything After, produced by T-Bone Burnett, was released in late 1993. The band toured extensively in 1993 and 1994, both as headliners and in supporting roles with other artists, including Cracker, the Cranberries, Suede, Bob Dylan, Los Lobos, Jellyfish, and Midnight Oil. The first single, "Mr. Jones," refers to The Himalayans bassist, who was Duritz's childhood friend; Marty Jones and Kenney Dale Johnson, the drummer of Silvertone, Chris Isaak's band, describing the desire of working musicians to make it big and the fantasies they entertain about what this might bring. Duritz sang the song in fun, enjoying the fantasy of making it big. However, he didn't realize that just months later, in December 1993, MTV began playing the video for the song. It was an unexpected hit song, drawing massive radio play and launching the band into stardom. August and Everything After became the fastest-selling album since Nirvana's Nevermind. With the turbo charge of their first single propelling the band forward, and positive reviews from Rolling Stone Magazine and other publications, it was decided that the band could use another guitarist, and Dan Vickrey, another Bay Area musician was offered the role as lead guitarist, singing backing vocals. The harmonies within the band drew praise from the start. In 1994 the band appeared on Saturday Night Live and Late Show with David Letterman, and toured with The Rolling Stones. The album sold 7 million copies, but success took a toll on the band; drummer Steve Bowman left, and Duritz suffered a widely-reported nervous breakdown, which was not his first.

The band played only two gigs in 1995. This allowed Duritz to write a set of songs that became the band's second album, Recovering the Satellites. Released October 15, 1996, it was heavier than August and Everything After, perhaps due to the addition of second guitarist Dan Vickrey, who had joined in early 1994. A response to the sudden fame that "Mr. Jones" had brought, it contains lyrics such as "These days I feel like I'm fading away / Like sometimes when I hear myself on the radio" (from "Have You Seen Me Lately?") and "Gonna get back to basics / Guess I'll start it up again" (from "Recovering the Satellites"). Dealing with the theme of Duritz's unease with his newfound fame, the album was described as "a concept album of sorts about trying to pick up the pieces of a family, a social life and a psyche shattered by fame."