The Rolling Stones recently kicked off their “50 and Counting…” tour in Los Angeles in a big way when they invited the idiosyncratic singer/songwriter Tom Waits to join them for a few numbers. For a few Stones fans who feel that they’ve let their stadium status go to their heads, performing with a singer as defiantly non-mainstream as Waits seems like a step in the right direction, but that got us thinking: what artists could have made amazing music together, but never got the chance to?

David Bowie and Marc Bolan: This is cheating a little bit, since Bolan actually played guitar on Bowie’s single “Prettiest Star” and the two remained great friends until Bolan’s death in 1977. But Bolan’s musical contribution to Bowie’s oeuvre came before Bowie had reached superstar status, and the notion of the glam titans collaborating for one glittery opus is just too hard to resist.

R.E.M. and Nirvana: After Nirvana hit it big with Nevermind, Kurt Cobain grew disdainful of the grunge sound that he had brought to the mainstream, especially after thousands of not-so-talented band flooded the charts with attempts to re-write “Smells Like Teen Spirit.” By 1994, Cobain was talking to R.E.M. singer Michael Stipe about a possible collaboration, with Cobain saying that Automatic For The People was one of his favorite albums. Sadly, Cobain died before a collaboration could be realized.

Yes and Led Zeppelin: The 1980s were a funny time for some of the hard rock and prog-rock bands that found success in the 1970s, with many groups either breaking up or writing more mainstream pop/rock songs. After breaking up Led Zeppelin, Jimmy Page and Robert Plant were determined to keep the spirit of hard rock alive with a collaboration with Chris Squire and Alan White, formerly of Yes. However, Page didn’t like the songs that Squire had written for the proposed supergroup (they were “too proggy,” apparently), and he cut the project short before it ever started.

Arcade Fire and Bruce Springsteen: Again, cheating a little bit here, since Bruce played live with the Arcade Fire back in 2007. Still, Arcade Fire play the sort of soaring, emotionally resonant rock that Springsteen practically invented, and their second album Neon Bible has the Boss’ fingerprints all over it. It’s actually a little surprising that more hasn’t come from this collaboration.

Interpol and Peter Hook: Look, Peter Hook has given up on New Order to play Joy Division songs with a group of touring musicians, and Interpol responded to the criticism of sounding a lot like Joy Division by sounding even more like Joy Division, so why not just put these guys in a room and let the magic happen. We’d personally rather hear Paul Banks sing “Love Will Tear Us Apart” than Hook’s somewhat weak Ian Curtis impression.