I carry a full toolbox under the bed in my travel trailer, and the only thing I've needed from it since 2013 has been the screw driver. Of course, if I took it out, then I would need a bunch of stuff.
x2 for midnightsadie's recommendation, the stuff needed to change a tire. Don't bother with your truck's jack, get a good quality bottle jack or if you have the room, one of those dolly / floor jacks. Also get a long breaker bar with the right size socket for your lug nuts, and leave it in the basement storage with the jack.