I cut my sandwiches like Cliffy! I also cut sub sandwiches and the like on a diagonal.
I don’t cut mine. Sometimes, if I’m feeling whimsical, I cut my husbands work sandwiches diagonally.
I fall strongly in the diagonal camp! I strongly prefer my sandwhiches this way and unless it would be an awkward social confrontation, I’ll continue it!
I do a compromise between diagonal and horizontal.
People who cut sandwiches are morally reprehensible. 
Diagonally. Sometimes twice if I want to “get in touch with my inner child”. Especially grilled cheese sammiches.
Diagonally, including subs (heroes, hoagies, and wedges). One deli owner I worked for pointed out that it’s easier to approach a nice pointy bite of wedge than a cross section of the middle which (unless your sandwich is made by an artiste who understands the imprtance of uniform distribution of sandwich filling all the way to the edge) is the thickest part.
Vertically.
Horizontally. That way, each half is narrow enough to be dunked in a glass of cold milk, and you can still have a solid grip on the part that isn’t submerged. I suppose this only makes a difference if your bread is wider than it is tall. Pepperidge Farm Farmhouse bread is much wider than it is tall.
It depends on the type of sandwich:
PB&J, usually diagonal
Grilled cheese, also diagonal, unless I’ve put tomato slices on it. Cooked tomatoes are too messy for a diagonal cut and slop off the pointed ends, so the sandwich gets cut into two rectangles or 4 squares. BLTs, same principle.
Sandwiches with chunks of meat (roast beef, salmon, chicken, etc.), two rectangles or 4 squares.
Tea sandwiches, especially those with hard-boiled eggs and raw tomato slices, are cut diagonally twice into 4 little triangles so they can be arranged nicely into pinwheels or “tents” on the plate. Tea sandwiches made with spreads (crab salad, for example) can also be cut into 6 little rectangular finger sandwiches.
If they’re for a packed lunch, I won’t cut them, since that only encourages them to fall apart inside the baggie.
Diagonally twice, so I end up with four neat little triangles.
I forgot about the almighty grilled cheese sandwich. I cut it on the diagonal and prefer to consume it with a pickle and a glass of chocolate milk.
Vertically! That’s the only way to do it - that or just leave it whole. With a lot of bread, if you cut it horizontally, then you’ve got one half that’s all round, and one half that’s all flat, and then the entire symmetry of the Sandwich Experience is ruined.
However, this does not apply to grilled cheese sandwiches, which get cut diagonally. That’s for the same reason why grilled cheese sandwiches need to be made with artificially, yellowy-orange cheese: It just is.
I cut mine the hard way, the cut running parallel to and between the slices of bread. But I’m thinking of changing, as it makes a big mess.
I mostly agree with Miss Mapp, but I change it up sometimes depending on my mood. Though, if I make sandwiches for the whole family at home, they will be cut differently depending on who is going to eat them, for example:
youngest son- vertical, crust removed
middle son- whole, crust occasionally removed depending on sandwich type
oldest son - diagonal
me - diagonal
husband - whole
I don’t cut them, unless they’re a big sub sandwich or something. I don’t see the point.
Vertically. Uncut sandwiches lose their fillings when I make them.
Now I want a grilled cheese sandwich.
I’m flexible. Usually I cut diagonally, unless the shape of the bread is not conducive to that cut, then I’ll either cut it vertically or not at all.
My preference is to trim the crust, make the sandwich and cut it into 1" squares. 
If it is such as to fall apart when cut then staples will hold it together. 
Not at all, and if I’m buying a 12-incher from Subway or the local Philly Steak shop I’ll often request from them my sandwich not be cut in half, either.