Can the sperm of one species impregnate another species

I was just wondering like if a dog humped a cat, would the cat still get pregnant?

In rare cases, such as the mule/hinny or the liger/tigon, one species can impregnate the other due to similar genes (they must be closely related animals, that is, relatively recently separated into their respective species in phylogenetic history). This still falls under the definition of a species, as the offspring are sterile and cannot continue the lineage.
The cat would not get pregnant because dogs and cats are not closely related enough for the egg of the cat to recognize the sperm of the dog. That'd be a pretty wicked mix though!

Actually, I believe some portion of the definition of what makes up a "species" includes whether or not members of the two species can interbreed and produce fertile offspring.

Some species that are relatively similar can produce offspring, but the offspring will generally be sterile. Mules are an example of this. You get mules by breeding horses with donkeys.

cats and dogs.... no....