Innie bellybuttons are said to comprise 90% of the belly button population, with outies making up the remaining 10%. The exact reason for this innie/outie belly button discrepancy remains a medical mystery, although there are some interesting theories floating around the Internet.
The belly button, also called the navel, is actually the body's first scar. The umbilical cord, which supplied nutrients to the unborn baby, is routinely clamped off shortly after the placenta has been expelled. Two clamps are placed a few inches away from the baby's body, and the cord is severed between them. The remaining vestiges of the umbilical cord eventually wither and fall off, leaving a small scar we know as the belly button. For many people, the scar is concave, meaning it recedes into the body. For others, the remaining scar tissue protrudes slightly from the body.
One theory holds that the innie belly button is the norm, while an outie is the result of a genetic aberration. Needless to say, this theory of natural selection does not enjoy widespread popularity among the outie belly button set. There is no scientific evidence to suggest that an outie is genetically preordained, or that an innie is the default setting once the umbilical cord falls off.
Another theory is that the doctor's handling of the umbilical cord can somehow influence the development of an innie or outie belly button. In reality, the umbilical cord is almost always clamped off several inches from the body, and the remaining cord cannot be manipulated surgically. Once it falls off, the belly button scar is set for life. A surgical outie to innie conversion is theoretically possible, but rarely performed.
Some believe that the outie belly button is the result of an abdominal hernia. If the muscles of the baby's abdominal walls collapse through weakness, a condition known as a hernia, then the baby's belly button may protrude instead of remaining concave. While the herniated condition is indeed possible, the chance of it permanently influencing the direction of a belly button is minimal. The belly button's innie or outie status is determined primarily by the formation of subcutaneous scar tissue, not damaged muscle tissue.
While we're on the subject, there are a few factoids concerning the formation of belly button lint that I feel compelled to share. The most common color of belly button lint is blue, primarily due to the prevalence of blue fibers in modern clothing. Belly buttons also attract more lint from below than from above. It's likely that more personal belly button lint came from your underwear and pants than from your shirt. I don't know what to do with this information personally, but you never know what might show up on a game show some day.