I've never even heard of a fluffy cheesecake! That sounds like a problem with the recipe more than the procedure. I could see it being fluffy if it had a lot of flour, leavening, or if it's a cottage cheese or ricotta cheesecake and you are used to cream cheese.

I use the supreme cheesecake recipe from Better Homes & Gardens. It's from a very old circa 1960/70 edition that I inherited from my grandmother. It comes out amazing, and definitely gets better the next day. It's also very simple, and doesn't require any special techniques. I just searched and found it online here:
http://www.keyingredient.com/recipes/13436168/cheesecake-supreme-better-homes-gardens/

If it's fluffy, I'll bet there is too much air in your batter. Try bringing your ingredients to room temperature before starting to mix them, use only low speed on your mixer and mix only until the ingredients are sufficiently blended. One other thing that I believe helps to make cheesecake creamy is to bake it in a water bath. One recipe I've had success with is the Philly Cream Cheese one.

Cook's Illustrated was the best cheesecake I ever made.
http://recipes.cooksillustrated.com/cakes-recipes/mid-atlantic/cheese/new-york-style-cheesecake-recipe/

http://labellecuisine.com/features/In%20Pursuit%20of%20the%20Perfect%20Cheesecake.htm

generally speaking there are two popular types of cheesecake. New York, and French. the NY cheesecake is the one that most people in the US are familiar with. the French cheesecake on the other hand, is a very light and fluffy thing.

in the case of the light and fluffy ones, a knife dipped in warm water might help.

it sounds like the recipe you are starting with is geared towards the french variety.

I use that one, too, and have never had a problem with it.

Sounds like too many eggs. This is the recipe I've been using, and it's the only one that I've used that I've been able to get a cheesecake that doesn't crack. Puts Junior's to shame.

http://www.cookingforengineers.com/recipe/89/Cheesecake-Plain-New-York-Style

I've encountered fluffy cheesecakes because the recipes call for folding in beaten soft/hard peak egg whites. My Barron's Cheesecake cookbook also suggests using dental floss to make clean cuts thru cheesecake which could help with this type of cake (mint flavor your call).
Best thing I've found are the foilware deep dish pizza pans which snugly fit around my springform pans. The contiguous foil completely protects the springform from water in the water bath and is nicely reusable. Now, I bake in a water bath all the time without fear of a water leak.
My newest favorite way to make the cheesecake mix is in my Vitamix blender. Just patterned off an included recipe and bam I'm blending up cheesecake on the smoothie setting and getting incredibly creamy, luscious cheesecakes-4 of them over the past holiday season. The one touch clean on the vitamix isn't too shabby either.

I will second the Cooks Illustrated recipe. It gives very clear instructions and technique tips. I made them for my wedding and they were lovely and dense. I believe it calls for more yolks and very little stirring.

I will also give the following suggestion, in case it is necessary: Full fat cream cheese. Full fat sour cream. Butter, not margarine. Eggs, not eggbeaters. Sugar not Splenda. Cream or half and half, not milk or fat free half and half.
There is a difference, and it will ruin your cheese cake.

I make sure my eggs and cream cheese are at room temperature. I like to cut on fat, half of the cream cheese is reduced fat, the other half is full fat. I bake my cheesecake in a water bath for 1 hour and then turn the oven off (with the cheesecake still inside) for 5-6 hours. Turns out perfect every time.

Like others have said, it could be the recipe that you are using.

I think the key to avoid it cracking in the oven is to put it in a "bagno Maria"

My family recipe for cheesecake uses only cream cheese, sour cream, sugar, eggs, and vanilla for the filling. It is dense and moist and wonderful, but my mother would disown me if I shared the recipe (there was an actual feud with an aunt over profligate disclosure).

My grandmother always told me to add the eggs one at a time, and wait to see that each one is fully incorporated before adding the next. Her cheesecakes were sought after by every bake sale and social event.

Hmm, very interesting. I recently had some fluffy cheesecakes and I quite liked them. I found the experience superior, even, to the denser cakes. Am I cheesecake ignorant?

I second (at least) the ATK/Cook's Illustrated recipe. It's great, and they also have a few yummy variations (pumpkin, marbled, lemon) if you're into that. I always get a nice smooth texture if I follow directions to the letter, which includes baking in a water bath and a very long cooling process where you cool in the water bath, then cool out of the water bath while periodically running a knife around the edge of the pan, then refrigerate. HOWEVER. Don't be like me and start this recipe at 9 PM, unless you want to be getting up every hour for the rest of the night. I really have done that a few times, such as on the night before Thanksgiving. The directions work, though. The gradual cooling process preserves texture and prevents cracking.

This recipe has always worked for us, and it tastes just like Cheesecake Factory! http://allrecipes.com/recipe/chantals-new-york-cheesecake/detail.aspx?event8=1&prop24=SR_Title&e11=chantals&e8=Quick%20Search&event10=1&e7=Recipe
I always felt the key was not to over mix and i always let mine sit a little bit before baking to make sure the air bubbles are out.

Oh, sorry and letting the cake cool for a few hours in the oven is key to a beautiful cheesecake!

I have always made cheesecakes well enough in advance to freeze them; much easier to cut when they are still partially frozen. I use a hot knife too. Every restaurant I've worked in, as well as my instructors in pastry school, used this method to get clean cuts. It makes plating easier too.

I use the three cities cheesecake recipe from Gourmet magazine or the cheesecake factory copycat recipe. I've found that they are fluffy when just baked but are best overnight in the fridge when it becomes dense and the favors meld. So be patient and wait overnight.

If your cheesecake is fluffy it might be that you are "whipping" it too hard when you combine your ingredients. Water bath is a GREAT THING to do to avoid cracking. But sometimes a little cracking happens anyway, which is why most of my cheesecakes get topped with some sweetened, flavored sour cream. Just a little smear over the top when it finishes baking, maybe with some vanilla or some gran marnier, or some lime juice or something like that.

I've also been known to cut the cream cheese with some chevre, about a 2/3 cream cheese 1/3 chevre combo-- really lightens the cake up without it being "fluffy". It makes a cheesecake that wont just kill your soul if you eat it on a hot summer day.