That depends on the specific gene in question.
Some genes are exactly the same in all members of a species (usually these code for incredibly essential proteins, if the protein were at all mutated the organism would die or not be able to reproduce).
Other genes (usually less essential ones - i.e., the genes that govern eye colour) have many different possible variations, so it becomes a problem in combinatorics to figure out which pair any specific organism inherits.
In general, there are two possible states:
1. The individual gets two copies of the same allele, one from each parent, in which case the individual is said to be "homozygous."
2. The individual gets two different alleles, one from each parent, in which case the individual is said to he "heterozygous."
Hope that helps.