Both, depending on the gene. Humans are diploid, carrying two copies of most genes (one from each parent). At any given gene location, a person is homozygous if the two copies (alleles) are identical and heterozygous if they differ.
Every person is homozygous at many loci and heterozygous at many others. Males are also hemizygous for most genes on the X and Y chromosomes, since they have only one copy of each.
Source: Zygosity — Wikipedia