Each cell can be owned by only one feature. As data, all cells must be able to hold the maximum cell value. Rasters are easy to understand, easy to read and write, and easy to draw on the screen. Grids are poor at representing points, lines and areas, but good at surfaces. Grids are good only at very localized topology, and weak otherwise.
Grids are a natural for scanned or remotely sensed data.
Grids suffer from the mixed pixel problem. Grids must often include redundant or missing data. Grid compression techniques used in GIS are run-length encoding and quad trees. Lines and areas are built from sequences of points in order. Lines have a direction to the ordering of the points.