3 ski straps and a multitool with appropriate screw drivers. I guess I also have spare ski pole bails that I don't usually bring, and wax, but I don't think of that as repair gear.
Apart from simple binding adjustments I've had a few situations in the backcountry:
* rear heel fell off: locked toes, pretended to be a telemarker and skiied out.
* brakes wouldn't lock in touring mode: big annoyance, nothing really bad happened, but skis sat in the shop for a few weeks after
* front pin sheared off: this was pretty bad, I tried to fix my boot to the ski with straps & somebody's paracord, but simply couldn't get anywhere near the amount of strength required, even for gentle skiing, and skis make really awkward snowshoes if your heel is fixed. On a long trip, it may be worthwhile to carry a spare binding toe.
* frozen binding parts: with enough patience, this can be solved, but a multitool/pocket knife/screw driver can speed up the process
I've never had a lost ski, but I highly recommend leashes over brakes: they're just way more simple with less that can go wrong about them.