Can a dog and cat breed?

Ummm no.

You may have just witnessed a display of dominance.

Or maybe it would be one of those "hybrid vigor" dogs? lol

Not at all. They could only produce offspring if they were very similar genetically. For example, there have been offspring of lions and tigers ("ligers"), and horses and donkeys sometimes produce mules, but the offspring are not able to reproduce. The closest I've heard of these is when a cat mates with a bobcat, or when a coyote mates with a dog (a coydog). Both are within the same family of animals and are very similar, so they can mate.

You didn't see them mating. You saw the dog MOUNTING the cat for domination purposes. No, they cannot be bred to produce a cat-dog or a dog-cat. If they do, you'll be one rich SOB!!

Absolutely not! Can you mate with an animal? 2 different species cannot mate.

In one word... NO. Cat's & dogs are different species and by definition different species of animals cannot produce offspring.

No, 2 completely different species.

You may have saw an act of dominance...

NO! They are different species and cannot breed and produce young.

It doesnt seem to stop them trying to though!

No thank-goodness or next we'd be seeing maltimanxes and maine coonadoodles.

omg this happened to me once!!! ok so i have a male beagle basset hound mix and he was humping my male cat named tubby...its happened more than once!! CRAZY!!

nope, just not possible. They each have different DNA which would not match up.