If you are referring to 2D arrays, then
YourArray(5,:) = [];
would delete row 5, and
YourArray(:,7) = [];
would delete column 7.
If you are referring to arrays with more than 2 dimensions then it is true that you cannot delete individual rows or columns in those arrays. In such a situation, though, you need to define what you want to have happen.
If I delete the upper-left-side row of a cube, then should a "hole" be left where it was, or should (as is the case for regular MATLAB arrays) something "move up" to fill that hole? If something should move, then what? At some point you would be left with a "hole" even if things moved, so what should happen if that hole is accessed? For example, is sum() of that "hole" 0 or the empty set?
The closest that MATLAB has to a list is cell arrays. Lists are, however, often circular or self-referencing, and cell arrays never are.
There is the MATLAB File Exchange contribution by Bruno that gives some (fragile!) pointer capabilities: see http://www.mathworks.com/matlabcentral/fileexchange/24576-inplacearray-a-semi-pointer-package-for-matlab
