How to make LEGO unbreakable
This is really nearly impossible unless you have a lifetime supply of super glue.

A good structure using Technic LEGO bricks will provide better support and a lot more "stick" to each other, making the creation less breakable. Building the structure in which the strongest side will take the most hits/pressure should be an excellent way to make the model unbreakable. Joining a Technic skeleton with other bricks should improve your model's durability. Technic and regular LEGO bricks create the best possible way for models to not fall apart.

Overlapping bricks (longer bricks preferred) like bricks can make a strong support for each other. Each piece helps each other support a piece, having no weak points unless layered unevenly. 

Try making your models fall and see where they break most often. The place where they break off is probably a weak point and needs more support or the pieces used are just too weak for the job. Replace/rebuild to improve the overall structure of the model. Of course, long bricks are preferred as the pressure is more evenly placed, making the hits seem pitiful against the strong model.