From a bike shop you can get pretty handy multitools. Usually they have a few Allen keys, and a screw driver or something. In my experience, you really just need the Allen wrenches. My bike kit has a small Allen wrench set, some tire levers, a spare tube, a small compressed air cartridge, and a valve that fits on the air cartridge so I can fill the spare tube. It's a small, light, and effective kit. The only thing I would add is a road rash first aid kit. Mostly just some gauze and tape. But if you're mostly mountain biking, maybe a bigger first aid kit would be good.
Wear a helmet, safety glasses, and gloves... Every time. You will appreciate it in the end.
Edit: Just to come full circle on your original question. I carried a Leatherman for a while, but it was just a waste of weight and space. I never needed any of the tools for riding.