Updated for all the new additions, let me know if I've missed any. The list is getting quite large, it's awesome to see this many teams accomplishing something awesome like this. Go programmers!
7-diskers:
33
70
118
341
469
624
987
1310
1477
1986
2054
2056
2415
2337
2474
2590
3539
3928
Hopefuls:
1241
1311
1678
3310