Alligator appeared on many year-end top 10 lists, including Uncut and Planet Sound, both of which ranked it as the number two album of 2005. Pitchfork ranked Alligator at number 40 in their top albums of the 2000s list. Alligator has sold over 200,000 copies worldwide.
The band performed album track "The Geese of Beverly Road" at the wedding of producer Peter Katis. A photo of the band performing on stage, with couples dancing in the foreground, became the cover of the band's next album Boxer.
The band supported Barack Obama's presidential candidacy in 2008. In July of that year, the band designed and sold a T-shirt featuring Obama's image above the words "Mr. November," a reference to both the closing track on the album and the month of the U.S. presidential election. All proceeds were donated to Obama's campaign. The song had been written, in part, about John Kerry's candidacy four years earlier.