I have heard that offspring can't grow taller than either of their parents but I've also heard that sometimes some gene activation can skip generations. Is it possible for a child to grow taller than their tallest parent?
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).
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)
Yes, people can definitely grow taller than their parents. Height is a polygenic quantitative trait (so affected by many genes), that is also strongly affected by environmental factors. You are also forgetting that there is a sex difference in height (~14 cm, Wright & Cheetham, 1999), so the height of the mother does for instance not set an absolute cap on the height of her sons ("....can't grow taller than either of their parents"), but her genetic background will influence their heights. If both parents are e.g. 180 cm tall, that is close to the population average for the father but considered tall for the mother, she is likely to carry genes that contribute to her offspring being tall.
That height is a polygenetic quantitative trait means that parental height will be a good predictor of offspring height, but with a wide scatter around the mean. Normally, 90% of children fall within 1.5 standard deviations of their midparental heights, after being sex-adjusted with +- 7cm for boys and girls (Wright & Cheetham, 1999). For simplicity, it is often said that 90% of children will fall within 10cm of the sex-adjusted mid-parental height. However, the deviations are smaller if the parents are unusually short or tall, representing "regression to the mean", and parental height is a poorer predictor for offspring height in these cases. Using the midparent mean as a predictor of offspring height is otherwise standard practice, as can be seen in online applications (e.g. http://medcalc3000.com/HeightPotential.htm). Using the same example as above, with both parents being 180 cm, will predict an offspring height of 186cm for sons and 174cm for daughters.
That height is strongly influenced by nutrition has been clearly shown in the general secular trend in body height in developed countries over the last centuries (Cole, 2003, where the average height of successive generations have been taller than their parents. For instance, the average height in the Netherlands have increased from 165 cm in 1860 to 181 cm in 1990 (numbers from Cole, 2003). Some of the online height calculators you see will also include a corrections for this, and add e.g. 1-2 cm to the mid-parent heights before correcting for sex.
Yes it is quite possible, recall nature vs nurture. I myself am slightly taller than both of my parents by about a head. As long as you have sufficient nutrition it should be quite possible.
And what you said about gene activation skipping generations is quite true- it can indeed happen, and if the gene responsible for height is not expressed in the parents but is in their offspring then it will also be more likely for the child to grow taller than their parent.