The way your teeth grow and how strong your teeth are depend on a number of factors. Birth defects and the natural structure of your face can cause orthodontic problems, and unforeseen circumstances can also change your skeletal structure in utero. But mostly, the way your teeth grow and align themselves is based on what kind of teeth you inherited.
Genetics is a very complex science, and is right now in that most interesting phase when it produces newer and newer mysteries to solve. We can say, though, that we inherit a mixture of genes from both of our biological parents. This means that you can inherit the tooth structure of your mother, or your father. But genetics can give you a mixture of the two, as the alleles responsible for making your teeth can in fact influence each other. This may make a new variation that is quite different from both your mothers or fathers set of chompers. You can also have a mutation, meaning a new and never before seen variation of the alleles that make your teeth, and this can be both positive or negative (though it tends to be the latter). You can also inherit recessive characteristics. A recessive characteristic is a given attribute that is not apparent in either the mother or father, but for which they both carry the gene for. This is why two brown haired people can sire a blonde baby, for instance.
This means that the status of your parents teeth is a pretty good indicator of what sort of teeth you will have, BUT, it is not a foolproof one. You could have a mutation, making your tooth alignment different from anything ever experienced, by your parents or otherwise, or you could have inherited a combination of recessive genes that may never have been expressed by anyone in your family!
This is quite rare, though, and usually, we all inherit teeth that are somewhat similar to everyone else in our families. There are certain traits that just get inherited more frequently, and this is also the case with inheriting the problems that our elders and the other members of our families have. So take a good look around, and see what kind of teeth people in your family have, it is a good way to prepare for what may lie ahead.