The first collection is called Kitchen Navigation. This collection requires the following five items:

Can Opener
Cutting Board
Salad Bowl
Simple Wine Opener
Wooden Spoon

Rewards for completion: 250 Cafe Points & 250 Coins

The next collection is Stainless Pots and Pans, and, as you might have guessed, you'll need to collect five different stainless steel cooking pans in order to turn it in. The five items are:

Stainless Frying Pan
Stainless Omlette Pan (this misspelling is native in the game)
Stainless Sauce Pan
Stainless Saute Pan
Stainless Skillet

Rewards for completion: 3 Six--hour Thymes & 500 coins (these Six-hour Thymes lessen the cooking time of any currently cooking dish by three hours)

The third collection is the Simple Dinnerware collection, that has you collecting four plates and one bowl through cooking. The five required items are:

Bread and Butter Plate
Dinner Plate
Salad Plate
Serving Dish
Soup Bowl

Rewards for completion: Unlock the Royal Feast recipe & 500 coins

The Royal Feast recipe is found on just the second page of the in-game Cookbook, under the "Fundamentals" section. It is a 12 hour dish, requiring 840 coins to cook. It offers 600 servings once completed, which are sold for 5 coins each, for a total of 3,000 coins in return. You'll earn 219 Cafe Points in the process of cooking and serving each Royal Feast.

The fourth collection is the Simple Pots and Pans collection. Not to be confused with the Stainless Pots and Pans collection above, these items are entirely different, basic versions of those stainless steel items. In this case, most of the pots are black, with some red and white accents. The five items are:

Frying Pan
Omlette Pan (again, this misspelling is also in the game)
Sauce Pan
Saute Pan
Skillet

Rewards for completion: 250 Cafe Points & 250 Coins

Finally, the fifth and last available collection (as of this writing), is the Cutting for Beginners collection. While this might sound like a class for those that are easily depressed, rather than a cooking collection, we'll give Zynga the benefit of the doubt here. This is, obviously, a knife collection, requiring the following knives:

Utility Knife
Chef's Knife
Paring Knife
Bread Knife
Carving Knife

Rewards for completion: +5 Energy points & 500 coins (Energy is used when preparing drinks and coffee for your guests before they sit down to dine on your current dishes)