Is it possible for a child to grow taller than their tallest parent?
People can grow taller than their parents. Anecdotally: I'm 185 cm, my parents are 155 cm and 178 cm. Joakim Noah, an NBA basketball player is 211 cm, his dad was 193 cm and mother was 175 cm... how?

Genetics and environment play a role in determining height. First of all, a more nutritious environment during development can lead to increased height, this is one reason why more recent generations appear to be taller.

Height is also an example of a quantitative trait - this means many genes (or loci [singular is locus], locations in the DNA) affect the phenotype (the physical measurable result i.e. a persons height). It is infact how the vast majority of traits are determined. At each locus that affects height there may be polymorphism (when more than one allele, or variant of that gene, exists).

Example:

Suppose height entirely is determined by 2 additive loci, $A$ and $B$, and no environmental effect occurs, and there is diploidy (two of each locus, one from each parent, determines height in a person). 

Each locus has two alleles denoted by $A_1$, $A_2$, $B_1 $ and $B_2$. Each copy of alleles $A_1$ and $B_1$ add 40 cm to a persons height, $A_2$ and $B_2$ add 50 cm to a persons height. 

Now a man who is $A_1 A_1, B_1 B_2$ (remember, humans are diploid) and a woman who is $A_2 A_1, B_1 B_1$ have children. Both parents are 170 cm tall. The theoretical limits for the population would be 160 cm and 200 cm. The children will inherit one copy of $A_1$ from the father and $B_1$ from the mother, but they could inherit either $B_1$ or $B_2$ from the father and either $A_1$ or $A_2$ from the mother. If a child inherited both of the taller alleles then they would be taller than the parents ($A_1 A_2, B_1 B_2$ = 180 cm). Likewise some offspring could be shorter.

Of course the reality is much more complex; height is determined by many more than 2 loci, by the environment, and gene * environment interactions. This principle was a hugely important because it meant that reproduction did not necessarily remove variation from the gene pool (a fundamental problem with early evolutionary theory was the thought of "blending" - when offspring are the average of their parents)