As a member of Generation X, it's impossible to not like Depeche Mode -- it was a constant soundtrack in high school, college, and beyond. While not to diminish the influence of their early work in their ongoing discography, for my money, it's hard to beat their three LP run of "Music for the Masses" (1987), "Violator" (1990), and "Songs of Faith and Devotion" (1993), all of which I plan to review here some day (tm).
There are dozens of songs with which we could recognize Andy Fletcher's passing, but I will take overlooked "Death's Door", from the excellent 1992 Wim Wenders soundtrack "Until the End of the World". Most of the soundtrack was original music, with some of the artists releasing the songs on later LPs. I don't think Depeche Mode ever released "Death's Door" on a regular studio LP, so other than B-sides and a single with remixes, I think the soundtrack is the only place you can hear it.
Depeche Mode - "Death's Door"