If I was limited to ONE edged tool to accomplish all of the chores I'd need to do, then my selection would be for a stout, carbon-steel-bladed, 9"+ fixed blade. That describes well my current survival knife, a Greco Explorer. I have used such a knife for survival purposed and know I could accomplish with it what I need to in order to stay alive.
Other knives which would fit that bill are the Cold Steel Trail Master (preferably with Carbon V steel), a Busse Battle Mistress, a Swamp Rat Battle Rat or variation, a Fehrman Final Judgment or any number of customs and prodcutions which have those specs.
Of course, in-town, I'd be mighty conspicuous walking around town with such a knife on my belt

Such was not the case a mere hundred years ago, but social engineering changes things... :grumpy:
To answer the original question, though, here's a list of the knives I could comfortably tackle all of life's chores with:
-slipjoint folder, such as a Queen mini-trapper in D2 or 1095
-3" folder. There are so many choices here like a Delica, CS 3" Voyager, or Mini-Griptillian
-3.5" folder. Various states set this as their legal limit for carry. A D2 Griptilian fits this bill
-4" folder. My favorite locking folder size. I'm still hunting around for the ideal production (read: affordable for a poor college student) 4" folder.
-3" fixed blade. An EDC fixed blade with a handle around 4" in length. I'm making some right now...
-4" fixed blade. The do-much knife while camping. Also useful in the kitchen.
-9" fixed blade. I really prefer a 9" fb to a 7" fb. I'm more comfortable with it and feel 9" of blade is more useful than 7".
-on-water knife. This would preferably have a 4" blade with partial serrations and stainless steel. I'd wear this when out on a lake or river.
-axe. full-sized. I need some way to chop the winter's firewood!
-axe. camp-sized. Right now, I'm shopping around. The Estwing 26" axe, while heavier, currently has my attention.
-multitool. They have such a wide range of uses, why not have one? In this category, I opt for my Leatherman Supertool 200. It's got the tools I need.
-SAK or Scout knife. The Farmer and Soldier models are my favorite SAKs, either of them would work fine. AG Russel makes a beautiful, 3.75" Scout knife which I've been eyeballing
So, I like having 4 fixed blades, 4 folders, and 4 tools. This list doesn't include kitchen knives, of course. In the kitchen, I like a paring knife and 8" or 10" chef's knife. A cleaver can be very useful, too.
Great thread, by the way!