There's only one species of domesticated dogs. of course you can cross different breeds and pure bred are far more valued.(Also note that there is some confusion here on THP as to what a hybrid IS. I say a hybrid is a cross between species, others say a hybrid is a cross between cultivars even if they are of the same species. According to them my mother has a hybrid dog! )
From a taxonomic perspective, hybrid refers to offspring resulting from the interbreeding between two animals or plants of different taxa.
1. Hybrids between different subspecies within a species (such as between the Bengal tiger and Siberian tiger) are known as intra-specific hybrids. Hybrids between different species within the same genus (such as between lions and tigers) are sometimes known as interspecific hybrids or crosses. Hybrids between different genera (such as between sheep and goats) are known as intergeneric hybrids. Extremely rare interfamilial hybrids have been known to occur (such as the guineafowl hybrids). No interordinal (between different orders) animal hybrids are known.
2. The second type of hybrid consists of crosses between populations, breeds or cultivars within a single species. This meaning is often used in plant and animal breeding, where hybrids are commonly produced and selected because they have desirable characteristics not found or inconsistently present in the parent individuals or populations. This flow of genetic material between populations or races is often called hybridization.