The subject is a minefield. 
  There are as many opinions as to what constitutes a good Cheesecake as there 
  are recipes. When I was a girl in California, there was only one sort served. 
  It was Vanilla flavored, made from Cream Cheese in a Graham Cracker crust, with 
  no topping. The place to find it was in one of the few bakeries which catered 
  to those who had relocated from the East Coast. I was utterly indifferent to 
  its charms. Then, on a visit to New York, a dear cousin took me to the famous 
  old Lindy's restaurant and I began to see the light. In short order I discovered 
  Italian Ricotta pies, and my search for new ways to enjoy this treat has never 
  ended.
  
  Some basics about Cheesecakes--
You must acquire a 9" 
  springform pan, since virtually all recipes call for one. A springform pan (sometimes 
  called a latch pan) is made in two pieces. One is a flat disc, and the other 
  is a ring, about 3 inches high, which fastens around the disc. The ring is controlled 
  by a lever which is a spring, hence the name of the pan. When something is made 
  in a springform pan, the disc becomes a base for the finished product. The sides 
  of the pan are removed, and the disc is placed on a serving plate with the Cake 
  upon it. If you want to give a party and serve several Cakes, buy several pans. 
  Please take my word for this. If you try to remove the Cake from the disc, it 
  will break, probably fall all over the place, and undoubtedly give rise to indelicate 
  language. You will also need another pan which is a few inches larger than the 
  springform one, and deep enough to hold about 2 inches of water.
When you are going to make 
  a Cake, turn the springform pan upside down, and wrap it with wide heavy-duty 
  Aluminum foil. Place the pan in the middle of the sheet of foil and press the 
  foil to it, up to the top. Springform pans leak, unless you do this. Most Cheesecakes 
  have a Crumb Crust which you will bake in the pan at 350 degrees for 8 minutes. 
  You will then pour the basic mixture on top of the Crust.
To bake the Cake, place 
  the large pan in an oven which has been preheated to 325 degrees, then place 
  the springform pan inside it. Pour hot water into the larger pan until it is 
  about 2/3 of the way up the sides of the springform pan. Then push the rack 
  into the oven and leave the cake alone for about 1 1/2 hours. DO NOT try to 
  do these machinations before you put the pan in the oven. If you try to lift 
  a pan filled with hot water and Cheesecake batter into the oven, you will slosh, 
  spill, get burned, and make a terrible mess. When the hot water sloshes on you, 
  you will drop the whole thing and it will take ages to clean everything. Although 
  you will sometimes see recipes which do not call for this method of baking in 
  a water bath, I wouldn't do without it. Cakes done without the waterbath run 
  the risk of being dry, and the cracks being much worse. (Most cheesecakes have 
  cracks, which is why you always see them with toppings, even the plain ones 
  do have something to mask the cracks)
When the Cake is done, 
  chill it before you remove the sides of the pan or try to cut into it in any 
  way. Although many things are very nice right from the oven, Cheesecake is not 
  one of them. The structure must be cold, before it is disturbed. To remove the 
  Cake, run a thin bladed spatula around the sides, then open the latch and remove 
  the ring.
I am certain that many 
  of you will want to know if there is a way to have Cheesecake without Fat and 
  Sugar. The answer is yes, and no. The texture of the finished Cake is dependent 
  upon the Fat content of the ingredients. If a recipe calls for Cream Cheese, 
  Cottage Cheese, or Ricotta Cheese: feel free to play with it and find the lowest 
  Fat version which is acceptable to your palate. You may substitute Non-Fat Evaporated 
  Milk for Whipping Cream, and use Low-Fat Sweetened Condensed Milk rather than 
  the full Fat sort. The texture WILL be different, but it may be fine to you. 
  A word of warning--Because the "mouth-feel" of low Fat Cakes is different, 
  there is a tendency to consume a great deal more in order to be happy. Do be 
  careful. About sugar--You may substitute a non-aspartame artificial sweetener 
  for up to half the sugar in baked cheesecakes. Do not use an aspartame based 
  sweetener, because it will break down with the application of heat. Unless you 
  are Diabetic, do not try to do away with Sugar altogether, because there will 
  be a large difference in both flavor and texture. Do not omit or lessen the 
  amount of Flour in these recipes. If you run across a recipe anywhere which 
  does not call for Flour, ignore it, unless you are a very accomplished baker. 
  Milk and Eggs both have long Protein molecules which curl together at high temperatures 
  in cooked mixtures, ergo curdling. The only sure way to prevent curdling is 
  by coating the molecules with Starch; that is why you should use Flour. Apply 
  this piece of advice if you are making any sort of Egg and Milk combination 
  which is cooked. A tablespoon of Flour added to a Custard will prevent disaster. 
  On to our recipes....
Crumb Crusts
  2 cups fine dry Crumbs from any flavor Cookie
  1/3 cup sugar
  1/3 cup melted Butter OR 2 Egg Whites
Method
  Mix the Crumbs with Sugar. Add either the melted Butter OR Egg Whites, and mix 
  thoroughly. Press into the bottom and partly up the sides of a springform pan, 
  or on the bottom and all the way up the sides of a 10 inch glass pie plate. 
  Bake at 350 degrees for 8 minutes. Remove from oven. Fill as directed in the 
  recipe. Either proceed with further baking, or chill and serve.
Basic Cottage Cheese 
  Based Cake
4 cups smooth whipped Cottage 
  Cheese
  1/3 cup Whipping Cream
  1 cup Sugar
  1/3 cup Flour
  2 teaspoons Vanilla extract
  1 teaspoon Almond extract
  5 Eggs, separated
Method
  In a large mixing bowl, beat the Egg Whites until stiff but not dry, and set 
  aside. In another mixing bowl, beat the remaining ingredients together until 
  smooth. Add one large spoonful of the beaten Egg Whites to the Cheese mixture, 
  and stir in, to "lighten" it. Pour the Cheese mixture into the bowl 
  with the rest of the beaten Egg Whites, and fold until completely combined. 
  Pour the Batter on top of a prepared Crumb Crust in a 9 inch springform pan. 
  Bake in a water bath at 350 degrees for 1 1/4 hours. Chill, remove the ring 
  from the pan, and serve. You may decorate the top of this cake with a tin of 
  any flavor prepared Pie Filling or sliced fresh Fruit.
Variations
Mocha
  Increase Sugar to 1 1/3 cups and Whipping Cream to 1/2 cup. Add 1/3 cup Cocoa 
  Powder. Dissolve 1 tablespoon instant Coffee Powder in the Extracts before adding. 
  Decorate the top with a bit of shaved Chocolate before serving.
Orange
  Use one teaspoon Orange extract in place of the Almond extract. Add 2 tablespoons 
  grated Orange Peel. Before serving, glaze with 1/2 cup melted Orange Marmalade.
Ginger
  Use Ginger Snap Cookies for the Crust. Add 4 teaspoons fresh grated Ginger Root. 
  Before serving, decorate the top with 1/2 cup finely chopped Candied Ginger.
Apple-Cinnamon
  Use 1 teaspoon artificial Maple extract in place of the Almond extract. Add 
  1 teaspoon Cinnamon. Before serving top with a tin of prepared Apple Pie filling.
Basic Cream Cheese 
  Based Cake
  4 (8 ounce) packages Cream Cheese, softened
  1 cup Sugar
  4 Eggs
  1/3 cup Flour
  2 teaspoons Vanilla extract
  1 teaspoon Almond extract
Method
  In a large mixing bowl, beat the Cream Cheese until very light and fluffy. Add 
  the remaining ingredients and beat until completely smooth. Pour on top of a 
  prepared Crumb Crust in a 9 inch springform pan. Bake in a hot water bath at 
  350 degrees for 1 hour. Chill, remove ring from pan, and serve. This may be 
  topped with a tin of prepared Pie Filling, or sliced fresh Fruit.
Variations
Chocolate
  Use 5 eggs. Melt 1 (12 ounce) bag Semisweet Chocolate Chips with 1/2 cup Whipping 
  Cream. Add to batter and beat thoroughly before pouring into Crumb Crust. Bake 
  as above. Decorate with sweetened Whipped Cream before serving.
Lemon
  Use 1 teaspoon Lemon extract in place of the Almond extract. Add 2 tablespoons 
  grated Lemon Peel. After pouring the batter into the Crumb Crust, pour over 
  it a jar of Lemon Curd which has been stirred until smooth. Swirl the Curd slightly 
  through the batter for a marbled effect. Bake as above. Decorate with sweetened 
  Whipped Cream before serving.
Pineapple
  Drain and squeeze the juice from 2 tins of Crushed Pineapple. Mix the drained 
  Crushed Pineapple into the batter before pouring into the Crumb Crust. Bake 
  as above. Before serving, decorate with Pineapple Slices.
Cappuccino
  Add 2 tablespoons Espresso Powder, 1 teaspoon Cinnamon, 1/4 cup Cocoa Powder 
  and 1/4 cup Whipping Cream. Use 2 teaspoons Rum flavored extract in place of 
  the Almond. bake as above. Before serving, decorate with shaved Chocolate and 
  sweetened Whipped Cream.
Individual Sized 
  Cheesecakes
You may prepare any of 
  the above cakes to be individually sized by this method. Line muffin cups with 
  foil liners. Don't use paper liners or the cakes will stick to them. in the 
  bottom of each liner place a small round cookie of any flavor you like. Pour 
  the batter on top of the cookies and bake at 350 degrees for 20 minutes. Chill, 
  remove from foil liners and serve.
Basic Carageenan-Based 
  Cheesecake
2 packets unflavored Carageenan-Based 
  Jelling Product
  1/2 cup boiling Water
  1 cup Sugar or Artificial Sweetener to equal 1 cup Sugar
  3(8 ounce size) packages cream cheese
  2(4 serving size) packages Vanilla flavor Instant Pudding Mix
  3 1/2 cups Milk
  1 cup Cookie Crumbs or chopped Nuts
Method
  Dissolve the Jelling product in the Water. In a large mixing bowl, beat together 
  the cream cheese and sugar or artificial sweetener. Add dissolved Carageenan, 
  and beat until until smooth. In another bowl, whisk together the Milk and Pudding 
  Mix. While beating, add the Pudding mixture to the cheese mixture and beat until 
  smooth. Pour on top of a prepared crumb crust in a 9 inch springform pan and 
  chill for 8 hours. When you are ready to serve, dip a knife in hot water and 
  run it around the side of the cake before removing the ring from the pan. Press 
  the Crumbs or Nuts into the sides of the Cake to decorate.
Variations
Strawberry
  Omit Sugar or Artificial Sweetener and Milk. Puree 3 packages frozen Strawberries 
  in Syrup in the blender. Measure 3 1/2 cups of the puree, and use in place of 
  the Milk. Chill as above and decorate with sweetened Whipped Cream or sliced 
  Strawberries.
Chocolate
  Use Chocolate flavor Instant Pudding Mix. Beat 1/3 cup Cocoa powder into the 
  Cream Cheese. Proceed as above. Decorate with shaved Chocolate
Banana
  Use Banana flavor Instant Pudding Mix and only 3 cups Milk. In the blender, 
  whir 3 Bananas with the Milk until smooth. Proceed as above. Decorate the Cake 
  with Banana slices which have been dipped in Orange Juice to prevent discoloration.