I am not a professional chef, but I do cook a lot, and am really into coffee, espresso and teas. I rarely have less than 50 types of tea at home, and the bar between my dining room likes like something you would find in a small coffee and tea house. Thus, while I'm not a trained expert, I have tried and enjoyed all the pairings below:

Weak Barley Tea served chilled is a fantastic match to Korean BBQ
Something about the barley really cuts through all of the strong sauces, spicy aftertastes, pickled vegetables and starchy rice to quench your thirst. The barley flavor also compliments the grilled marinated meats.

Jasmine tea goes really well with Thai food, and matches the flavor of the Jasmine Rice. The hint of floral sweetness pairs nicely with the spicy food, much like how slightly sweet wines often compliment spicy dishes.

Iced Southern Sweet Tea (I use a mixture of black tea and dried rose petals) compliments BBQ like nothing else. The sweetness with the hint of floral goes nicely with the spicy tangy and smoky flavor of the BBQ meat. The black tea base gives it enough kick to power through the other flavors on your palate so that the flavor of the tea isn't lost.

A strong hot brew of barley tea, ginger tea and honey can compliment a variety of slightly sweet desserts. It is served at a Vietnamese Bakery I like. The mostly server mild French style pastries topped with sliced fruits or a small amount of custard, so the desserts are a bit milder and less sweet than what you would find in an American bakery. The strong spicy ginger and the heavy honey sweetness sort of rounds out the experience and makes up for the milder flavored dessert.

Ceylon Black Currant Tea (black tea flavored with black currants) with cream can make a great compliment to heavy sweet desserts. Things like sticky toffee pudding have an almost overwhelming sweetness, but the bitterness of the tea helps relieve the palate, much like how espresso goes nicely with sweet chocolate cake or tiramisu. The hint of fruity sweetness from the currants takes the edge of the bitterness and reinforces the idea that you are having a decadent dessert.
http://www.englishteastore.com/1mt-bc.html

Strong black tea, such as English Breakfast, Irish Breakfast and other black blends go nicely with heavy salty greasy breakfasts. The acidity and strength helps cut through the salt and grease and provides a satisfying compliment to breakfasts similar to coffee. The bitterness can also balance out the sweetness of common breakfast sides such as toast with jelly, pancakes with syrup, etc.
http://en.wikipedia.org/wiki/Irish_Breakfast_tea

Market Spice or other sweet and spicy teas compliment coffee cakes, pumpkin bread and similar cakes. The spices of the team compliment and amplify the spices in the breads.
http://www.pacificnorthwestshop.com/pnwfoods/marketspicetea.htm

Bitter Green tea with Japanese food. Teriyaki, Sukiyaki, Tonkatsu sauce and many varieties of sushi have a bit of sweetness to them. The bitter green tea balances the sweetness and acts as a sort of palate cleanser to help you appreciate the flavor of the next bite.
http://en.wikipedia.org/wiki/Sencha

Mild Iced fruit flavored black teas go nicely with salads. Salad greens often tend to be bitter, and the mild fruitiness of the tea helps neutralize and compliment the bitterness. The dressing often tend to be salty, and the black base of the tea offers enough bitterness to balance out the salt.
http://www.republicoftea.com/templates/detail.asp?navID=8

Hot Black Ceylon Tea with Cardamom (iced or hot) goes nicely with Persian food. Many of the flavored Persian rices have fruits such as orange rind, dates, cherries and other slightly sweet foods. The bitterness of the black tea helps balance this sweetness. The cardamom adds just a hint of spice that blends nicely with the aftertastes if mildly spiced kabobs and koobideh.
http://sadaf.com/store/product603.html