Live, Beck has covered "Black Math." Jack White has shown up at a couple of Beck concerts over the years, joining in on "Cold Brains," "99," and "Last Fair Deal Gone Down." Beck showed up once at a White Stripes concert to play bass on "The Denial Twist." Jack has also covered a few of Beck's songs on stage on occasion.
In the studio, Jack White plays bass on "Go It Alone." Beck produced (in his living room, no less), and played, on a Stripes single with these songs: "Honey, We Can't Afford To Look This Cheap," "It's My Fault For Being Famous," and "Cash Grab Complications On The Matter."
Beck was in a White Stripes music video for "The Hardest Button To Button," and then a number of years later, The Stripes released Beck's remix of the song.
More recently, Beck recorded "I Just Started Hating Some People Today" and "Blue Randy" in Jack's studio. Jack plays on both tracks, and released them as a single on his record label. Supposedly, Beck recorded an entire album in Jack's studio, which we're still waiting on.