I'm one of those people who think that each of the activities listed deserves its own tool, and there are knives that do those functions better than others.
CAMPING: I tend to like fixed blade knives that are good slicers and excel at food preparation and can also be used in preparing kindling and other simple chores. I've been using the Becker BK10 for this, though it is a bit beefy for a good slicer.
HIKING: I tend to prefer a lightweight folder worn in a sheath on my belt. My favorite is the Rittergrip here.
HUNTING: I haven't hunted in a looong time - mostly in my teenage years with my buddie who lived on a farm. At that time I preferred a fixed blade that was VERY sharp and had a sweeping curved blade that facilitated skinning. Back then I used a Buck Special 119.
BACKPACKING: I haven't backpacked since my days in Boy Scouts, but from what I've read, the preferred knives are all small and relativley lightweight. These inlcude small SAKs or Leathermen like the Micra or Squirt.
FISHING: I see two different primary uses for knives related to fishing. One is what I think of as general cleaning of fish. For this I prefer a smallish fixed blade knife so it doesn't get too gunked up. Beyond that, just about any blade will do for scaling and head-choping. Now, if you choose to do filleting (I never do) then certainly a thin fixed bladed fillet knife is certainly called for.
Will one knife do all this? Well, the knife that comes to mind is one of the Mora knifes. They are light enough to carry while hiking & maybe backpacking, good enough slicers for camping, and probably could do a half-decent job filleting a fish. I have the Model 22, but I'd rather not use an oil-sealed wooden handled knife for butchering game or cleaning fish. Models 731 or 741 (carbon or stainless) from
http://www.ragweedforge.com seem like they'd do well. For my taste (the other plastic handled Moras on the site are a bit too short for food preparation and fish cleaning.