Except in the case of X inactivation in females, and genes on the Y chromosome in males, generally speaking _both_ alleles are expressed in cells.
A good example is the ABO blood type marker system. If the mother is type AA, she will pass on an _A_ allele, which codes for the A antigen. If the father is type BB, he will pass on a _B_ allele, coding for the B antigen. Therefore, any children will be type AB, as the maternal chromosome 9 will express the A form, and the paternal chromosome 9 will express B.