Capping a stone wall is an important part of building many stone structures, including stone arch bridges. The trouble is, the top of a stone wall is the most vulnerable part of the whole wall. Whereas stones at the bottom of the wall are rendered more or less immovable due to the weight of the masonry above, the capping stones on the wall have little holding them in place, save their own mass. Fortunately, there are several simple schemes that can help hold everything in place.
Use Mortar
If the wall is mortared, it will be less vulnerable to damage from dislodged stones. The mortar helps “glue” the stones together and increase friction, helping to prevent accidents. However, the top stones really should still be reasonably large (see below) to help prevent damage. For a mortarless build, of course, mortar is not an option. The obvious expedient of mortaring only the top stones in place is a bad idea, as a mortarless structure is perpetually shifting, all but guaranteeing rapid failure of mortar above.
Large Stones
The most common way of capping a stone wall is with massive, flat stones. The sheer weight of these stones renders them more or less immovable. Of course, the stones need to be well set in place and tight fits for stability. This is probably the most common method of capping a stone wall. It works well, too, though there are other options available.
Pegging the Wall Together
A very old method of ensuring the stability of a masonry structure is to peg the stones together. Holes were drilled into the stones, and small dowels of either stone or metal were added. These dowels join a course of stone to one or more courses below, and tend to prevent sliding from occurring. Any metal used should never be iron, as iron not only rusts, but when rusting expands, which can break the stones. Pegging the stones can help prevent individual stones from being dislodged, and could be used in the capping of a wall with success. However, there are still plenty of other solutions.
Concrete Cap
Where function is more important that form, capping a stone wall with a solid slab of concrete, ideally reinforced, is a highly stable option, quite effective for mortarless structures. Concrete does work extremely well, but is not always the most sightly way to cap a stone wall.

Being a strong, solid mass, especially if reinforced, concrete capping will be much better able to handle the shifting of a mortarless build than a mortared stone wall atop such a structure would.
Sod-Capped Walls
A very old, venerable method of stabilizing mortarless walls is to place a layer or two of sod atop the wall. Popular in old Scottish work, the sod provides additional weight to the wall and thereby stabilizes the last layer of stones. Over time, of course, the sod forms a solid mass atop the structure. This method actually works quite well. A traditional way of capping a wall with sod is to place the sod two layers deep. The bottom layer is placed upside down, while the top layer is placed right side up. Even in more modern masonry texts from the early 20th century, capping a mortarless wall with sod was considered acceptable practice.

Alternatively, piling loose soil atop the wall will help stabilize the structure. The soil will pack down over time, and its weight will help prevent stones from being dislodged.
Herringbone Walls
A herringbone wall is a wall made with stones laid propped up with a long end up, and laid at an angle. This type of construction is popular in traditional Irish stonework. Obviously, an individual stone laid with a long side up is unstable, even without leaning. However, put a row of stones leaning this way against each other and the wall becomes a solid mass, as each stone is now leaning on its neighbor. A wall built this way can be several layers deep, perhaps with each alternate layer leaning in the opposite direction from the one immediately below. Alternatively, a herringbone wall one layer deep can be added atop a more conventionally built stone wall to cap it. An obvious problem, however, with a herringbone wall is that it must end somehow. Leaning stones must have something to lean against. Usually, a leaning row of stones meets up with another leaning line of stones that is leaning in the opposite direction, the two leans cancelling each other out. A small triangular section of stonework is inserted where the two oppositely leaning walls meet. As far as the other end of things is concerned, namely the part of the wall where the row of leaning stones begins, it is not uncommon to see a massive stone or two placed such that the bottom of the herringbone wall is pushing against them. These large stones keep the base of the tilting stones from sliding out.

The herringbone wall tends to defy dislodging impacts as each individual stone is firmly locked against its neighbors. The obvious weak point of such a construction is at the ends of the wall where the chain of leaning stones begins. Therefore, the end stones that stabilize the herringbone wall should be massive.
Sloped Walls
One occasional difficulty found when building a masonry wall is how to build it sloped. This difficulty stems from the fact that stones rely on gravity to hold them in place. A slope in the wall will tend to make the wall unstable, unless it is sloping against something immovable. The traditional method used in these scenarios is to build the walls in steps like a staircase.

By building the wall in steps, gravity still pushes each stone straight down, and yet the wall be built up slope or be built with a sloped top. The capping stones, then, should follow the steps and not be built at a slope.