How do I stop getting punctures on my bike?

Throw a bone our way... getting flats and throwing slime in the tube doesn't explain your situation well. What kind of riding? How heavy are you? Paved or dirt/gravel? Back or front tire? How many flats in what span of time? Are you replacing the tube or patching? Leaks on inside, outside or left/right sides of tube. What kind of tires? BMX, MTB, road, race...?