In a city where most forms of entertainment are forbidden on theological grounds, shopping has been raised to a kind of art form, and you can get just about anything imaginable in Riyadh.
Gold is one of the best purchases you can make -- and this is also true in the rest of the Gulf as well. You pay the going London spot price per ounce plus no more than 10% for workmanship. The savings are spectacular: I paid $85 for a pair of hoop earrings for my wife, who saw virtually identical ones in Minneapolis for almost $600!
Tailors are also very cheap. If you have some time -- say 10 days -- take a favorite garment to a good tailor and ask him to copy it using the fabric you've provided. A man's shirt costs around $10 to have made.
Watches are often very good deals, too. Arabs LOVE watches, so you can find every brand you can think of and usually at prices much lower than anywhere in the West.
Perfume is an excellent buy as well. Arabs can't live without it and you can find any imaginable scent. Be sure to go to Gazazz, which is Saudi's best perfume shop. They give away amazing free samples, too!