Going from 15" rims to 16" rims will only raise your car 1/2" (not a full 1" as some might expect). You won't even notice the change. It would be cheaper just to buy tires with a different profile. For example:
Old tires: 225/60R15 have an overall diameter of 25.6" (rim dia + tire dia)
New tires: 245/70R15 have an overall diameter of 28.5" (rim dia + tire dia)
That would raise your vehicle 1.5". Still not enough for you to notice.
You'll have to address wheel well clearances and speedometer variations no matter which direction you take.
Sure, you may be able to go to a 16 rim and tire package, but it will completely depend the specific year, make and model of vehicle your own. What are you driving? If going to 15 inch to 16 rims you have to change tires as well. Depending on you automobile this can easily be calculated. Go to tirerack.com. Plug in your automobile info. Select the 16 wheel options. You will see your needed rim size and tire size as well.
You have to buy new wheels that fit your car are are correct for the tires. When done correctly, you select a lower profile tire so the outside diameter is the same. There will be no height increase. This will preserve the proper gearing etc. for the car.
Depends on what you're talking about, im going to assume car and answer the question as that. Its going to depend on the clearance you have, really thats it for the most part.
new rims and tires
I have 15 inch tires I want to get 16 inches just to have more of a height when I am sitting. Can I just change the tires, or do I have to do something before hand?