Reading Victor Papanek and James Hennessey's inspiring 1974 Nomadic Furniture 2 and looking at the interesting "Jim's Peg-Lock System" on p. 108, I got to thinking about camlocks as a substitute for screws.
Jim's Peg-Lock System inserts a short wooden dowel into a round hole through a square piece intersecting a wooden dowel of the same size run through another round hole in the same square piece at right angles to it --- slightly skew to it but without enough distance between their axes to prevent interference. This is reportedly explained in more detail in Nomadic Furniture 1 pp. 126-7; from this volume, though, it's not clear whether you cut a bite out of the other dowel or just compress the heck out of the wood. If there's a bite out of the other dowel, it will be under no force, but cannot be withdrawn from its hole unless the peg is removed. If there's no bite, or a bite that's slightly too small, the wedging mechanical advantage is potentially enormous.
This got me to thinking about the celt, a type of stone axe, and oval dowels. If you stick an oval dowel in an oval hole made to fit it loosely, it can slide linearly but binds up if you start rotating. If you apply further force, you may be able to get it to rotate 90°, depending on how oval it is. (In the circular limit, the mechanical advantage is infinite, but the displacement is zero, so the force is limited by the sponginess of the wood.)
If the short axis of the oval hole runs across the grain of the wood, then the rotated oval dowel will be pressing against endgrain, like a well-made celt; in this configuration it will not fall out from moisture changes and will not tend to split the wood. At the 90° rotation angle, it is in an equilibrium; it does not have a tendency to twist back one way or the other. There are no stress risers because the wooden surfaces are smoothly curved. Some kind of wax, drying oil, or soap might be a good way to lubricate the initial assembly in a way that stabilizes it further without making disassembly impossible; glue would make the joint permanent.
If instead the oval hole's long axis is parallel to the wood grain and a slit cut is made to the end of the wood, through the oval hole, and some distance beyond, the rotation of the wooden dowel can force the holed wood to expand laterally, pressing on the inside of some other slot or hole, rather like a wedge tenon, but reversible. If the slot or hole is closer to the fulcrum than the hole is, this can provide a further mechanical advantage. An unoccupied round hole at the base of the slit can eliminate stress risers there and increase compliance for this use.
Alternatives to an unobtainium oval dowel might include two round dowels with equal flats cut on one side and face-glued, and an eccentric round dowel, like a crankshaft. The eccentric round dowel is easier if the two cylinders are of different sizes so that one is entirely contained in the hypothetical extension of the other. This crank configuration, if used to power a prismatic joint by sliding in a slot, provides a variable mechanical advantage that reaches a zero-displacement singularity, like a Vise-Grip or similar toggle linkage. If movement is permitted a bit past this singularity and then stopped, for example by the end of the slot, it can support a stable equilibrium not dependent on friction and thus not vulnerable to vibration.
A similar stable equilibrium can be provided in the oval-hole mechanism by pooching out the sides of the oval hole a bit at the ends of the short axis, thus converting the unstable equilibrium into a stable equilibrium (with unstable equilibria near it on each side), and eliminating the need for linseed oil or whatever as a form of wood Loctite.
If, instead of sliding against the wall of a slot near the end of its travel, the eccentric dowel is rolling another disc or dowel along a track, it may be possible to make this mechanism work without any sliding friction, just rolling friction. If the two eccentric arcs are cut into opposite edges of a piece of material, it may be possible to make the entire wedging mechanism planar with sheet cutting.
Mechanisms like these are viable alternatives to screws in many situations.