Thank you for asking such an interesting question!
The answer is that wires can technically be made into square or triangle shapes or whatever you want, they just don't tend to be. First, let's look at how wires are made:
Basically, if you want to make a wire, you take metal and draw it through a mold that has a hole in it. You might do this several times to get the gauge of wire that you want, but you can technically make the mold any shape that you want. The thing is that you have to remember that most types of wires fill a specific purpose. For example, wire is commonly made for necklaces and is more comfortable than square wire would be (because of the edges) on the skin. Wire for dental braces is the same way.
If you are talking more about electrical wiring, I can think of two reasons. First, a lot of electrical wiring is not a solid piece of metal but is really made up of many, many tiny threads of wire twisted together. This makes the wires more flexible, and round wires are better for this purpose because they will fit more closely together (unless somebody takes the time to stack each square wire properly against each-other.) Secondly, when a wire is threaded through wood or a hole in the wall the hole has usually been made by a drill with a round bit. The wire will go much more easily through a hole in the wall that is round if it is indeed round as well. Just think of that goofy toy we used to play with as babies with the round holes and the square pegs.
Hope this helped!
Why are doors made the shape they are and not cylindrical? Because doors are designed for people to pass through.
The same way, wires are designed for electricity to pass through them. Electricity is the flow of millions of electrons and the shape of an electron is the shape of a very small ball. So for these balls to pass easily the best wire should be cylindrical.