Credited to singer Mick Jagger and guitarist Keith Richards, "Don't Stop" was largely the work of Jagger. Writing began during Jagger's preparations for his 2001 album Goddess in the Doorway. At the time of release, he commented, "For me, doing a solo album or a Stones album is all the same, with one proviso: that when I'm writing for the Rolling Stones I don't mind if the song sounds like the ones the Stones do, whereas if I'm writing, but not recording with the Rolling Stones, I don't want the song to contain too many of the clichés that one associates with the Rolling Stones, so I try quite hard to avoid them. Before the release of Forty Licks, I wrote 'Don't Stop' in the same period that I was writing the songs for my solo album, and I just put it to one side and said to myself, 'This sounds very much like the Rolling Stones to me. It might be very useful in the coming months, but I'll leave it for now and I won't record it because I think it's going to be better for the Stones.'"
A straightforward rocker featuring a trademark opening riff from Richards, "Don't Stop" tells of a rough love affair between the singer and his lover:
The way you bit my lip and you drew first blood, It warmed my cold, cold heart; And you wrote your name right on my back, Boy, your nails were sharp
Well I'm losing you, I know your heart is miles away; There's a whisper there where once there was a storm; And all that's left is that image that I've filed away, And some memories have tattered as they've torn
Recording began on "Don't Stop" in the early summer of 2002 at Guillaume Tell Studios, in Suresnes, France. On the recording, Richards said at the time, "['Don't Stop' is] basically all Mick. He had the song when we got to Paris to record. It was a matter of me finding the guitar licks to go behind the song, rather than it just chugging along. We don't see a lot of each other. I live in America, he lives in England. So when we get together, we see what ideas each has got: 'I'm stuck on the bridge.' 'Well, I have this bit that might work.' A lot of what Mick and I do is fixing and touching up, writing the song in bits, assembling it on the spot. In 'Don't Stop', my job was the fairy dust." With Jagger on lead vocals, both Richards and Ronnie Wood accompany on guitars. "Don't Stop" is one of the many later Stones songs to feature Jagger on rhythm guitar. Wood provides the two solos near the middle and at the end. Charlie Watts plays drums, Darryl Jones bass, and Chuck Leavell keyboards.
Released on 16 December 2002, "Don't Stop" reached number 36 on UK Top 75 Singles and number 21 on the 'Billboard Mainstream Rock Tracks chart. The song was performed heavily during the 2002–2003 Licks Tour in support of Forty Licks.