Do tall people have more cells?
This is really the most fundamental concept of Cell Biology, so good question. If you look at the size of a any cell from a whale and compare it to the size of any of cells from a mouse, they are in fact quite similar, despite the extreme difference in the overall size of the organisms they are from. There is a reason why cells are small, and it has to do with the fact that they survive based on their ability to absorb enough nutrients from their environment. As a cell gets larger it needs more to survive (because it has a bigger mass). A bigger cell has also has a larger surface area around it (so it can absorb more nutrients).

HOWEVER, there gets to be a point where the mass of the cell is too large for the surface area to compensate for. Mathematically this is shown by what is called the "surface-area-to-volume ratio". Basically, it states that as a a sphere gets larger, the volume increases at a higher RATE than the surface area. So there is a reason cells get only so big, the 60's horror movie The Blob was not scientifically accurate, a single-cell that large (the blob) would not have enough surface area to absorb enough nutrients to sustain itself. Taller (or bigger) people have more cells (not bigger ones) than others.

Effects of osmotic pressure can alter cell size slightly.

When you are talking about taller individuals, you are (I think) really meaning larger people, people with a higher mass. And yes, they have more cells.

Another topic of Cell Biology you may want to explore is apoptosis. Let's say you have two individuals both 180 lbs. one of them is 5' tall and the other 7'. Both these individuals have the same number of cells, but the taller one has a higher percentage of them in the superior and inferior regions of the body. It is the process of apoptosis that sculps an organisms shape.