Most trampolines sold in sports and recreation stores are round in shape and it is in fact somewhat difficult to find a square trampoline without purchasing it from online. You may think that there is no difference between a square and a round trampoline other than their shape but they do in fact have some differences that should be considered when you are choosing a trampoline for your family.
The reason the round shaped trampoline is so much more prevalent is because it is inherently easier to use. Especially for younger children or those with little experience on a trampoline, a round shape will help you to stay centered on the trampoline and avoid falling off or getting caught in the springs where injuries can occur. Round trampolines have more give to them giving a softer bouncing experience and less chance of errantly flying from the trampoline due to an unbalanced bounce. Because of the shape and the configuration of the springs you will always be pushed towards the center of a circular trampoline which is somewhat of a safety feature.
Square and rectangle shaped trampolines offer a slightly different bouncing experience. You may have noticed that Olympic trampolines used by gymnasts are rectangular in shape. Square trampolines operate with the same principles. Because of the configuration of the springs and the square shape, these trampolines have a tighter bounce that can lead to much higher air with experienced bouncers. They also offer less variation in the bounce from the middle to the sides but lack the centering effect of a circular trampoline. This means that it is easier for an inexperienced user to accidentally fall off or get to close to the edge possibly landing on the springs. One benefit of a square trampoline is that it uses space more efficiently and will take up less room in your backyard.
Unless you are using your trampoline as a skilled gymnast there is really no reason to buy a square trampoline. For recreational purposes a round one is a it safer for most users. For whatever type of trampoline you wish to purchase, there are safety accessories such as mesh cages that can be fitted to any trampoline.