Answer
Most human cells are between 10 and 15 micrometers wide.
Egg and (some) fat cells are bigger than this range. Additionally some nerve and muscle cells are much longer, even though they are not very wide.
Cells cannot grow much larger since a cell that is too big cannot support itself.
Work Step by Step
As a cell's dimensions expand, the volume increases much faster than the increase in surface area. The cell takes in nutrients through its cell membrane. At some point, the cell is unable to take in enough nutrients to support itself. This puts a limiting factor on how large cells can grow.
Most cells are between 10 and 15 micrometers wide. Egg cells are larger. Fat cells (when saturated) are also larger. Some muscle and nerve cells are incredibly long (up to 30 cm) since they run a significant length of a person's body. These muscle and nerve cells, however, are also very narrow, increasing the surface area to volume ratio and allowing for the cell to take in enough nutrients.
