How many times are dogs mentioned in the Bible?

I can think offhand of two occasions in the Old Testament. When David approaches Goliath, Goliath asks "am I a dog that you're coming to with sticks?" Also, raw unclean meat is to be thrown to the dogs (Exodus 23?)

The SwordSearcher program comes up with 15 uses of the word "dog" and 24 uses of "dogs" in the King James Version.

Greyhounds are the only breed of dogs mentioned in the Bible, in Proverbs 30: 29-31

That's a mistranslation. The Hebrew mentions lions, wild boars and goats, but no dog.

It may well be a mistake in translation but the question was not specific about which version of the bible.

Proverbs 30: 29-31 reads: -
There be three things which go well, yea,
Which are comely in going:
A lion, which is strongest amongst beasts and
Turneth not away from any;
A Greyhound;
A he-goat also.

Four centuries ago scholars knew much less about the ancient languages than they do today. In some cases the translators faced words they had never seen before. They could only guess at the meaning. That's why the King James Version, in Proverbs 30:31, says "greyhound" when it should say "rooster," and in Job 30:29, it says "dragon" when it should say "jackal."

Modern Hebrew isn't all that different from biblical Hebrew. A few small differences in the grammar but even those are small differences only. The Hebrew word "zarzir" which is translated as "greyhound" in the King James bible, is really one of the Hebrew words for wild boar. The word for rooster is "Sechvi" or "Tarnegol". Also, the King James bible was compiled in England, where the wildlife was considerably different from that of the Middle East, and different animals symbolized different things.