Za'atar is a Middle Eastern spice blend, usually a combination of thyme, sesame seeds, marjoram, oregano, salt, and other spices depending on which country you're in. This aromatic spice mix is also very versatile. It goes great on chicken and other meats as a seasoning, but it's also terrific as a condiment. I recommend sprinkling it over grilled pita with some olive oil drizzled on top. You could also mix it into labane - a Middle Eastern yogurt/cheese - with some olive oil. Another quick, easy, and delicious idea is to sprinkle some za'atar with some shredded mozzarella on a pita and a little olive oil and heat it up in the oven for a few minutes for a tasty, and quick snack.
Schug is a Yemenite hot pepper mixture popular in Israel. It combines either red or green peppers with coriander, garlic, and other spices. If you go to a falafel place and they ask if you want hot sauce, chances are it's schug they are offering. Israelis might use the Hebrew name harif, but it's the same thing. That spicy hummus you see in the store? It's probably flavored with schug. I personally like the red pepper mixture better than the green, but I recommend trying both.
I have a terrific recipe that uses schug with harissa - another Middle Eastern hot pepper mix, which I'll get into later - as a spice rub on chicken. I'll get to that one soon.
Now, where can you get these items? If you are fortunate enough to live near a kosher market, chances are good that it will stock both of these items. Your local supermarket might also carry them in its kosher section, or a local Middle Eastern store will likely have them. If none of those options work out, you can always turn to the Internet and mail-order.