Kuwait and Jordan are the two countries that border both Iraq and Saudi Arabia. If you count territorial waters as well, then Iran borders both Iraq (over land) and Saudi Arabia (across the Persian Gulf at the maritime border).
Saudi Arabia and Oman
All of the Gulf countries do share a border with Saudi Arabia (except the island of Bahrain which is off of the Saudi coast), but there is no "requirement" that Gulf countries border Saudi Arabia.
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The two countries on Iraq's southern border are Saudi Arabia and Kuwait.
The UAE is bordered by Oman and Saudi Arabia.
Yemen and Oman border Saudi Arabia to the south.
yemen
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Two. Iraq and Saudi Arabia.
qatar borders Saudi Arabia and Bahrain
Yemen and Oman.
Middle Eastern countries do not have counties.